Question

For each problem, find an example of an equation that would work with the following criteria

1. The two x-intercepts are 2 and 10. The y-intercept is -12

2. The Axis of Symmetry is x = 4. The y-intercept is 28

3. The Axis of Symmetry is x = -3. The y-intercept is 24.

4. The x-intercepts are 8 and -4. The y-intercept is 16.

Answer 1

1. y = 0.6x² - 7.2x + 12

2. y = x² - 8x + 28

3. y = x² + 6x + 24

4. y = -0.5x² + 2x + 16

Explanation:

1. The two x-intercepts are 2 and 10. The y-intercept is -12

A(x - 2)(x - 10)

A(x² - 12x + 20)

20A = 12

A = ⅗ = 0.6

y = 0.6x² - 7.2x + 12

2. The Axis of Symmetry is x = 4. The y-intercept is 28

(x - 4)² + C

x² - 8x + 16 + C

16 + C = 28

C = 12

y = (x - 4)² + 12

y = x² - 8x + 28

3. The Axis of Symmetry is x = -3. The y-intercept is 24.

(x + 3)² + c

x² + 6x + 9 + C

9 + C = 24

C = 15

y = x² + 6x + 24

4. The x-intercepts are 8 and -4. The y-intercept is 16.

A(x - 8)(x+ 4)

A(x² - 4x - 32)

-32A = 16

A = -0.5

y = -0.5x² + 2x + 16