Question

Type the correct answer in each box. Use numerals instead of words.

Answer 1

Answer:

f(x) = 2x(x - 8)

f(x) = 2(x - 2)² - 8

Step-by-step explanation:

Let the equation of the quadratic function is,

f(x) = a(x - h)² + k

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

From the graph attached,

Vertex of the parabola → (2, -8)

Therefore, equation of the function will be,

f(x) = a(x - 2)² - 8

Since, the graph passes through origin (0, 0),

f(0) = a(0 - 2)² - 8

0 = 4a - 8

a = 2

Equation of the given parabola will be,

f(x) = 2(x - 2)² - 8

      = 2(x² - 4x + 4) - 8

      = 2x² - 8x + 8 - 8

      = 2x² - 8x

      = 2x(x - 8)

Therefore, factored form of the function will be,

f(x) = 2x(x - 8)