Question

Write the equation of each parabola in vertex form a. Vertex: (-3, 7); Point:(-2, -5) b. Vertex: (1, 3); Point: (2, 5) c. Vertex: (-4, 6); Point: (-2, -2) d. Vertex: (7, 4); Point: (5, 16)

Answer 1

Answer: a) y = 2(x + 3)² - 7

              b) y = -2(x + 4)² + 6

              c) y = 3(x - 7)² + 4

Step-by-step explanation:

The vertex form of a quadratic equation is:  y = a(x - h)² + k     where

• "a" is the vertical stretch
• (h, k) is the vertex
• (x, y) is any point on the curve

Input (h, k) and (x, y) to solve for "a"

a)  (h, k) = (-3, 7)   and   (x, y) = (-2, -5)

    -5 = a(-2 + 3)² - 7

     2 = a(1)²

     2 = a

                y = 2(x + 3)² - 7

b)  (h, k) = (1, 3)   and   (x, y) = (2, 5)

    5 = a(2 - 1)² + 3

     2 = a(1)²

     2 = a

                y = 2(x - 1)² + 3

c)  (h, k) = (-4, 6)   and   (x, y) = (-2, -2)

    -2 = a(-2 + 4)² + 6

    -8 = a(2)²

    -8 = 4a

    -2 = a

                y = -2(x + 4)² + 6

d)  (h, k) = (7, 4)   and   (x, y) = (5, 16)

    16 = a(5 - 7)² + 4

    12 = a(-2)²

     12 = 4a

      3 = a

                y = 3(x - 7)² + 4