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=-(b)/(2 a)`

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

Substituting these values, we get;

`x=-((-10))/(2(-1))`

Simplifying the terms, we get;

`x=-(-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.