Question

Write the quadratic function g(x)=x2−8x in standard form.

A) g(x)=x^2−8x
B) g(x)=x2+8x
C) g(x)=x2−8
D) g(x)=x2+8

Answer 1

To write the function g(x) = x^2 - 8x in standard form, we complete the square to get g(x) = (x - 4)^2 - 16, which is the vertex form of the parabola with vertex (4, -16).

Step-by-step explanation:

To convert the quadratic function g(x) = x^2 - 8x into standard form, we must complete the square to transform it into the vertex form of a quadratic equation, which is g(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

1. Start with the original equation: g(x) = x^2 - 8x.
2. Divide the coefficient of the x-term by 2 and square the result to get the complete square term: (-8 / 2)^2 = 16.
3. Add and subtract the square term inside the equation: g(x) = x^2 - 8x + 16 - 16.
4. Factor the perfect square trinomial: g(x) = (x - 4)^2 - 16.
5. Now, we have the standard form of the quadratic function: g(x) = (x - 4)^2 - 16.

This gives us the vertex form of the parabola, where the vertex is (4, -16), and the parabola opens upwards since the coefficient of (x - 4)^2 is positive.