Question

Write a quadratic function in

standard form whose graph
satisfies the given condition(s).
1. X-intercepts: - 1 and 1
2. vertex (8,8)
3. passes through (-5.0), (4,0).
and (3, -16)

Answer 1

The quadratic function in standard form is -0.5(x - 8)^2 + 8.

Step-by-step explanation:

To write a quadratic function in standard form, we can start by finding the factors of the quadratic equation based on the given information.

The x-intercepts are -1 and 12, which means the factors would be (x + 1) and (x - 12).

The vertex is (8,8), so the equation would have the form a(x - h)^2 + k, where (h, k) is the vertex.

Substituting the vertex values, we get a(x - 8)^2 + 8.

Finally, we can use the point (4,0) to solve for 'a' and find the final quadratic function.

Using the point (4,0), we can substitute x = 4 and y = 0 in the equation a(x - h)^2 + k.

This gives us the equation a(4 - 8)^2 + 8 = 0.

Solving this equation, we find that a = -0.5.

So, the quadratic function in standard form that satisfies the given conditions is -0.5(x - 8)^2 + 8.