Question
consider the graph of the following quadratic equation. y = -x^2 - 10x + 24
What is the y-value of the vertex?
What is the y-value of the vertex?
Answers
GPT 3.5
To find the y-value of the vertex of a quadratic equation in standard form (y = ax^2 + bx + c), we can use the formula for the x-coordinate of the vertex:
x = -b/(2a)
In this case, a = -1 and b = -10, so:
x = -(-10)/(2*(-1))
x = 10/(-2)
x = -5
Now that we have the x-coordinate of the vertex, we can plug it back into the original equation to find the y-value:
y = -(-5)^2 - 10(-5) + 24
y = -25 + 50 + 24
y = 49
Therefore, the y-value of the vertex is 49.
x = -b/(2a)
In this case, a = -1 and b = -10, so:
x = -(-10)/(2*(-1))
x = 10/(-2)
x = -5
Now that we have the x-coordinate of the vertex, we can plug it back into the original equation to find the y-value:
y = -(-5)^2 - 10(-5) + 24
y = -25 + 50 + 24
y = 49
Therefore, the y-value of the vertex is 49.