Question

consider the graph of the following qudratic equation. y= -x^2 -10x + 24.What is the y-value of the vertex?

Answer 1

Given that the quadratic equation is $y=-x^{2}-10 x+24$

We need to determine the y - value of the vertex.

The x - value of the vertex:

The x - value of the vertex can be determined using the formula,

$x=-\frac{b}{2 a}$

where $a=-1, b=-10, c=24$

Substituting these values, we get;

$x=-\frac{(-10)}{2(-1)}$

Simplifying the terms, we get;

$x=-\frac{-10}{-2}$

$x=-5$

Thus, the x - value of the vertex is -5.

The y - value of the vertex:

The y - value of the vertex can be determined by substituting the x - value of the vertex ( x = -5) in the equation $y=-x^{2}-10 x+24$

Thus, we get;

$y=-(-5)^{2}-10(-5)+24$

Simplifying the values, we have;

$y=-25+50+24$

$y=49$

Thus, the y - value of the vertex is 49.