Question

Write the function in standard form. ​f(x)=-4(x-9)^2 11

Answer 1

To write the function in standard form, we need to expand the square term and combine like terms.

Step 1: Expand the square term

f(x) = -4(x-9)^2 + 11

f(x) = -4(x^2 - 18x + 81) + 11

Step 2: Distribute the -4

f(x) = -4x^2 + 72x - 324 + 11

Step 3: Combine like terms

f(x) = -4x^2 + 72x - 313

Therefore, the function in standard form is:

f(x) = -4x^2 + 72x - 313

Answer 2

The function f(x) = -4(x-9)² + 11 is already in standard form for a quadratic function. The standard form of a quadratic function is f(x) = a(x-h)² + k, where (h, k) is the vertex of the parabola, and a is a coefficient that determines the direction and steepness of the parabola. In this case, the vertex of the parabola is at (9, 11), and the coefficient a is -4, which means the parabola opens downwards and is steeper than if a were 1 or -1.

Explanation: