Question

Write the following in the form Ax^2+Bx+C=y

Answer 1

13). y = x² + 6x + 8

14). y = 2x² + 8x - 12

Explanation:

13). Vertex form of a parabola is given by,

y = a(x - h)² + k

Here (h, k) is the vertex of the parabola.

Equation of a parabola with vertex (-3, -1) will be,

y = a(x + 3)² - 1

Since, y-intercept of the parabola is y = 8

In other words, parabola is passing through (0, 8)

8 = a(0 + 3)² - 1

8 = 9a - 1

9a = 9

a = 1

Therefore, equation of the parabola will be,

y = (x + 3)² - 1

y = x² + 6x + 9 - 1

y = x² + 6x + 8

14). Equation of a parabola with vertex (-2, -20)

y = a(x + 2)² - 20

Since, y-intercept of the parabola is (0, -12),

-12 = a(0 + 2)² - 20

-12 + 20 = 4a

4a = 8

a = 2

Therefore, equation of the parabola will be,

y = 2(x + 2)² - 20

y = 2(x² + 4x + 4) - 20

y = 2x² + 8x + 8 - 20

y = 2x² + 8x - 12