Question

A quadratic equation can be written in the form =(−ℎ)2+ y = a ( x - h ) + k , where (h, k) is the vertex of the parabola. This form can be used to determine the minimum y-value of the related function. Which is the minimum y-value of =52−20+24 y = 5 x 2 - 20 x + 24 ?

Answer 1

To find the minimum y-value of the quadratic function y = 5x^2 - 20x + 24, calculate the vertex using the formula h = -b / (2a). For this equation, the vertex is (2, 4), meaning the minimum y-value of the function is 4.

Step-by-step explanation:

To find the minimum value of the quadratic function y = 5x2 - 20x + 24, we first need to identify the vertex of the parabola. The vertex form of a quadratic equation is y = a(x - h)2 + k, where (h, k) is the vertex. We can find the x-coordinate of the vertex (h) by using the formula h = -b / (2a).

In this case, a = 5 and b = -20, so:

h = -(-20) / (2 * 5)
h = 20 / 10
h = 2

Now that we have the x-coordinate of the vertex, we can find the y-coordinate (k), which is the minimum value of the function for a parabola that opens upwards (since a > 0).

Plugging h into the original equation to find k:

k = 5(2)2 - 20(2) + 24
k = 5(4) - 40 + 24
k = 20 - 40 + 24
k = 4

Therefore, the minimum y-value of the function is 4, which occurs at the vertex (2, 4).