Graphing Quadratic Functions Worksheets - Free Printable

Here are the completed tables and instructions for sketching the graphs for each quadratic function.

1) $f(x) = -x^2 + 4x - 2$

Step-by-step Calculation:
* $x = 0$: $-(0)^2 + 4(0) - 2 = -2$
* $x = 1$: $-(1)^2 + 4(1) - 2 = -1 + 4 - 2 = 1$
* $x = 2$: $-(2)^2 + 4(2) - 2 = -4 + 8 - 2 = 2$
* $x = 3$: $-(3)^2 + 4(3) - 2 = -9 + 12 - 2 = 1$
* $x = 4$: $-(4)^2 + 4(4) - 2 = -16 + 16 - 2 = -2$

Table Values:
| x | 0 | 1 | 2 | 3 | 4 |
| :--- | :---: | :---: | :---: | :---: | :---: |
| f(x) | -2 | 1 | 2 | 1 | -2 |

Graph Sketch: Plot the points $(0, -2), (1, 1), (2, 2), (3, 1), (4, -2)$. Connect them with a smooth curve that opens downward (like an upside-down U). The highest point (vertex) is at $(2, 2)$.

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2) $f(x) = x^2 + 8x + 13$

Step-by-step Calculation:
* $x = -6$: $(-6)^2 + 8(-6) + 13 = 36 - 48 + 13 = 1$
* $x = -5$: $(-5)^2 + 8(-5) + 13 = 25 - 40 + 13 = -2$
* $x = -4$: $(-4)^2 + 8(-4) + 13 = 16 - 32 + 13 = -3$
* $x = -3$: $(-3)^2 + 8(-3) + 13 = 9 - 24 + 13 = -2$
* $x = -2$: $(-2)^2 + 8(-2) + 13 = 4 - 16 + 13 = 1$

Table Values:
| x | -6 | -5 | -4 | -3 | -2 |
| :--- | :---: | :---: | :---: | :---: | :---: |
| f(x) | 1 | -2 | -3 | -2 | 1 |

Graph Sketch: Plot the points $(-6, 1), (-5, -2), (-4, -3), (-3, -2), (-2, 1)$. Connect them with a smooth curve that opens upward (like a U). The lowest point (vertex) is at $(-4, -3)$.

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3) $f(x) = x^2 - 2x - 2$

Step-by-step Calculation:
* $x = -1$: $(-1)^2 - 2(-1) - 2 = 1 + 2 - 2 = 1$
* $x = 0$: $(0)^2 - 2(0) - 2 = -2$
* $x = 1$: $(1)^2 - 2(1) - 2 = 1 - 2 - 2 = -3$
* $x = 2$: $(2)^2 - 2(2) - 2 = 4 - 4 - 2 = -2$
* $x = 3$: $(3)^2 - 2(3) - 2 = 9 - 6 - 2 = 1$

Table Values:
| x | -1 | 0 | 1 | 2 | 3 |
| :--- | :---: | :---: | :---: | :---: | :---: |
| f(x) | 1 | -2 | -3 | -2 | 1 |

Graph Sketch: Plot the points $(-1, 1), (0, -2), (1, -3), (2, -2), (3, 1)$. Connect them with a smooth curve opening upward. The lowest point (vertex) is at $(1, -3)$.

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4) $f(x) = -x(x + 2)$ which simplifies to $-x^2 - 2x$

Step-by-step Calculation:
* $x = -3$: $-(-3)(-3 + 2) = 3(-1) = -3$
* $x = -2$: $-(-2)(-2 + 2) = 2(0) = 0$
* $x = -1$: $-(-1)(-1 + 2) = 1(1) = 1$
* $x = 0$: $-(0)(0 + 2) = 0$
* $x = 1$: $-(1)(1 + 2) = -1(3) = -3$

Table Values:
| x | -3 | -2 | -1 | 0 | 1 |
| :--- | :---: | :---: | :---: | :---: | :---: |
| f(x) | -3 | 0 | 1 | 0 | -3 |

Graph Sketch: Plot the points $(-3, -3), (-2, 0), (-1, 1), (0, 0), (1, -3)$. Connect them with a smooth curve opening downward. The highest point (vertex) is at $(-1, 1)$.

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5) $f(x) = -(x - 4)^2 + 5$

Step-by-step Calculation:
* $x = 2$: $-(2 - 4)^2 + 5 = -(-2)^2 + 5 = -4 + 5 = 1$
* $x = 3$: $-(3 - 4)^2 + 5 = -(-1)^2 + 5 = -1 + 5 = 4$
* $x = 4$: $-(4 - 4)^2 + 5 = -(0)^2 + 5 = 5$
* $x = 5$: $-(5 - 4)^2 + 5 = -(1)^2 + 5 = -1 + 5 = 4$
* $x = 6$: $-(6 - 4)^2 + 5 = -(2)^2 + 5 = -4 + 5 = 1$

Table Values:
| x | 2 | 3 | 4 | 5 | 6 |
| :--- | :---: | :---: | :---: | :---: | :---: |
| f(x) | 1 | 4 | 5 | 4 | 1 |

Graph Sketch: Plot the points $(2, 1), (3, 4), (4, 5), (5, 4), (6, 1)$. Connect them with a smooth curve opening downward. The highest point (vertex) is at $(4, 5)$.

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6) $f(x) = x^2$

Step-by-step Calculation:
* $x = -2$: $(-2)^2 = 4$
* $x = -1$: $(-1)^2 = 1$
* $x = 0$: $(0)^2 = 0$
* $x = 1$: $(1)^2 = 1$
* $x = 2$: $(2)^2 = 4$

Table Values:
| x | -2 | -1 | 0 | 1 | 2 |
| :--- | :---: | :---: | :---: | :---: | :---: |
| f(x) | 4 | 1 | 0 | 1 | 4 |

Graph Sketch: Plot the points $(-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4)$. Connect them with a smooth curve opening upward. This is the standard parabola with its vertex at the origin $(0, 0)$.

Final Answer:
See the calculated tables and graph descriptions above.