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