Question

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

Answer 1

To convert the quadratic function g(x) = -2(x-5)^2 + 17 into standard form, we expand the square and simplify. The resulting standard form of the quadratic function is g(x) = -2x^2 + 20x - 33.

Step-by-step explanation:

The quadratic function given is in vertex form, which is g(x) = a(x-h)^2 + k, where (h, k) is the vertex of the parabola. To convert this into standard form, which is ax^2 + bx + c, we need to expand the square and simplify. The given function is g(x) = -2(x-5)^2 + 17.

Let's expand this:

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• First, square the binomial: (x-5)^2 = x^2 - 10x + 25
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• Next, multiply by -2: -2(x^2 - 10x + 25) = -2x^2 + 20x - 50
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• Finally, add the constant 17: -2x^2 + 20x - 50 + 17 = -2x^2 + 20x - 33

Therefore, the quadratic function in standard form is g(x) = -2x^2 + 20x - 33.