Question

A quadratic function is represented by g(x)=-2(x-5)^2+17 what is the equation for this function in standard form

PLS HELPP

Answer 1

The standard form of the given quadratic function is:

`g(x)=-2x^2+20x-33`

Explanation:

The standard form of a quadratic function is f(x) = ax² + bx + c.

To write the given function in standard form, expand the brackets:

`\implies g(x)=-2(x-5)(x-5)+17`

`\implies g(x)=-2(x^2-10x+25)+17`

Apply the distributive law: m(a + b + c) = ma + mb + mc

`\implies g(x)=-2x^2+20x-50+17`

Add the numbers: -50 + 17 = -33

`\implies g(x)=-2x^2+20x-33`

Answer 2

• g(x) = - 2x² + 20x - 33

---------------------------

Given function:

• g(x) = -2(x - 5)² + 17

This is the vertex form and the standard form is:

• y = ax² + bx + c

Convert the given equation into standard form:

• g(x) = - 2(x - 5)² + 17 =
• - 2(x² - 10x + 25) + 17 =
• - 2x² + 20x - 50 + 17 =
• - 2x² + 20x - 33