Graphing quadratic functions in intercept form worksheet with labeled x-intercepts, axis of symmetry, vertex, and y-intercept for three example problems.

Let’s solve each problem step by step. We’ll find the x-intercepts, axis of symmetry, vertex, y-intercept, and one more point for each quadratic function.

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Problem 1: y = (1/2)(x + 4)(x - 2)

✔ X-intercepts:
Set y = 0 → (1/2)(x + 4)(x - 2) = 0
So, x + 4 = 0 → x = -4
or x - 2 = 0 → x = 2
→ X-intercepts: (-4, 0) and (2, 0)

✔ Axis of Symmetry:
Midpoint between x-intercepts:
x = (-4 + 2)/2 = -2/2 = -1
→ Axis of symmetry: x = -1

✔ Vertex:
Plug x = -1 into the equation:
y = (1/2)(-1 + 4)(-1 - 2) = (1/2)(3)(-3) = (1/2)(-9) = -4.5
→ Vertex: (-1, -4.5)

✔ Y-intercept:
Set x = 0:
y = (1/2)(0 + 4)(0 - 2) = (1/2)(4)(-2) = (1/2)(-8) = -4
→ Y-intercept: (0, -4)

✔ One more point:
Pick x = 1:
y = (1/2)(1 + 4)(1 - 2) = (1/2)(5)(-1) = -2.5
→ Point: (1, -2.5) — or you could pick x = -2, etc.

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Problem 2: y = -(1/2)x(x - 8)

✔ X-intercepts:
Set y = 0 → -(1/2)x(x - 8) = 0
So, x = 0 or x - 8 = 0 → x = 8
→ X-intercepts: (0, 0) and (8, 0)

✔ Axis of Symmetry:
Midpoint: x = (0 + 8)/2 = 4
→ Axis of symmetry: x = 4

✔ Vertex:
Plug x = 4 into equation:
y = -(1/2)(4)(4 - 8) = -(1/2)(4)(-4) = -(1/2)(-16) = 8
→ Vertex: (4, 8)

✔ Y-intercept:
Set x = 0 → y = -(1/2)(0)(0 - 8) = 0
→ Y-intercept: (0, 0) — same as one x-intercept

✔ One more point:
Pick x = 2:
y = -(1/2)(2)(2 - 8) = -(1/2)(2)(-6) = -(1/2)(-12) = 6
→ Point: (2, 6)

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Problem 3: y = (x + 2)(x - 2)

This is a difference of squares: y = x² - 4

✔ X-intercepts:
Set y = 0 → (x + 2)(x - 2) = 0
→ x = -2 or x = 2
→ X-intercepts: (-2, 0) and (2, 0)

✔ Axis of Symmetry:
Midpoint: x = (-2 + 2)/2 = 0
→ Axis of symmetry: x = 0

✔ Vertex:
Plug x = 0 into equation:
y = (0 + 2)(0 - 2) = (2)(-2) = -4
→ Vertex: (0, -4)

✔ Y-intercept:
Set x = 0 → y = (0 + 2)(0 - 2) = -4
→ Y-intercept: (0, -4) — same as vertex

✔ One more point:
Pick x = 1:
y = (1 + 2)(1 - 2) = (3)(-1) = -3
→ Point: (1, -3)

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Final Answer:

Problem 1:
- x-intercepts: (-4, 0), (2, 0)
- Axis of symmetry: x = -1
- Vertex: (-1, -4.5)
- y-intercept: (0, -4)
- Additional point: (1, -2.5) [example]

Problem 2:
- x-intercepts: (0, 0), (8, 0)
- Axis of symmetry: x = 4
- Vertex: (4, 8)
- y-intercept: (0, 0)
- Additional point: (2, 6) [example]

Problem 3:
- x-intercepts: (-2, 0), (2, 0)
- Axis of symmetry: x = 0
- Vertex: (0, -4)
- y-intercept: (0, -4)
- Additional point: (1, -3) [example]