Here are the solutions for each quadratic function on your worksheet. I have calculated the vertex, axis of symmetry, solutions (x-intercepts), y-intercept, domain, and range for every problem.
1. $f(x) = -x^2 + 3x + 4$
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Opens up/down: Down (because $a$ is negative)
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Vertex: $(1.5, 6.25)$
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Axis of symmetry: $x = 1.5$
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Solution(s): $x = -1, x = 4$
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y-int: $(0, 4)$
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Domain: All real numbers
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Range: $y \le 6.25$
2. $f(x) = x^2$
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Opens up/down: Up
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Vertex: $(0, 0)$
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Axis of symmetry: $x = 0$
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Solution(s): $x = 0$
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y-int: $(0, 0)$
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Domain: All real numbers
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Range: $y \ge 0$
3. $f(x) = x^2 + 5x + 4$
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Opens up/down: Up
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Vertex: $(-2.5, -2.25)$
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Axis of symmetry: $x = -2.5$
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Solution(s): $x = -4, x = -1$
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y-int: $(0, 4)$
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Domain: All real numbers
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Range: $y \ge -2.25$
4. $f(x) = \frac{1}{2}x^2 - 2x - 6$
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Opens up/down: Up
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Vertex: $(2, -8)$
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Axis of symmetry: $x = 2$
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Solution(s): $x = -2, x = 6$
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y-int: $(0, -6)$
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Domain: All real numbers
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Range: $y \ge -8$
5. $f(x) = -\frac{1}{4}x^2 + 3x - 5$
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Opens up/down: Down
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Vertex: $(6, 4)$
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Axis of symmetry: $x = 6$
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Solution(s): $x = 2, x = 10$
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y-int: $(0, -5)$
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Domain: All real numbers
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Range: $y \le 4$
6. $f(x) = \frac{1}{3}x^2 + 2x$
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Opens up/down: Up
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Vertex: $(-3, -3)$
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Axis of symmetry: $x = -3$
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Solution(s): $x = -6, x = 0$
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y-int: $(0, 0)$
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Domain: All real numbers
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Range: $y \ge -3$
7. $f(x) = -\frac{1}{3}x^2 - x + 6$
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Opens up/down: Down
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Vertex: $(-1.5, 6.75)$
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Axis of symmetry: $x = -1.5$
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Solution(s): $x = -6, x = 3$
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y-int: $(0, 6)$
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Domain: All real numbers
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Range: $y \le 6.75$
8. $f(x) = 2x^2 - 4x + 2$
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Opens up/down: Up
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Vertex: $(1, 0)$
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Axis of symmetry: $x = 1$
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Solution(s): $x = 1$
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y-int: $(0, 2)$
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Domain: All real numbers
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Range: $y \ge 0$
9. $f(x) = x^2 - 8x + 12$
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Opens up/down: Up
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Vertex: $(4, -4)$
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Axis of symmetry: $x = 4$
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Solution(s): $x = 2, x = 6$
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y-int: $(0, 12)$
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Domain: All real numbers
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Range: $y \ge -4$
10. $f(x) = x^2 + 4x + 4$
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Opens up/down: Up
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Vertex: $(-2, 0)$
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Axis of symmetry: $x = -2$
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Solution(s): $x = -2$
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y-int: $(0, 4)$
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Domain: All real numbers
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Range: $y \ge 0$
11. $f(x) = x^2 + 7x + 10$
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Opens up/down: Up
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Vertex: $(-3.5, -2.25)$
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Axis of symmetry: $x = -3.5$
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Solution(s): $x = -5, x = -2$
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y-int: $(0, 10)$
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Domain: All real numbers
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Range: $y \ge -2.25$
12. $f(x) = -x^2 + 3x + 10$
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Opens up/down: Down
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Vertex: $(1.5, 12.25)$
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Axis of symmetry: $x = 1.5$
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Solution(s): $x = -2, x = 5$
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y-int: $(0, 10)$
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Domain: All real numbers
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Range: $y \le 12.25$
13. $f(x) = -x^2 + 6x - 5$
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Opens up/down: Down
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Vertex: $(3, 4)$
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Axis of symmetry: $x = 3$
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Solution(s): $x = 1, x = 5$
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y-int: $(0, -5)$
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Domain: All real numbers
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Range: $y \le 4$
14. $f(x) = -\frac{1}{2}x^2 - 5x - 8$
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Opens up/down: Down
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Vertex: $(-5, 4.5)$
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Axis of symmetry: $x = -5$
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Solution(s): $x = -8, x = -2$
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y-int: $(0, -8)$
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Domain: All real numbers
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Range: $y \le 4.5$
15. $f(x) = \frac{1}{2}x^2 - 4x + 6$
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Opens up/down: Up
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Vertex: $(4, -2)$
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Axis of symmetry: $x = 4$
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Solution(s): $x = 2, x = 6$
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y-int: $(0, 6)$
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Domain: All real numbers
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Range: $y \ge -2$
Parent Tip: Review the logic above to help your child master the concept of using a calculator worksheet.
