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, we need to first convert the quadratic equation into vertex form. The vertex form of a quadratic equation is given by y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.
Given equation: y = -x^2 - 10x + 24
To convert this into vertex form, we need to complete the square. First, factor out the coefficient of x^2:
y = -(x^2 + 10x) + 24
Now, complete the square for the expression inside the parentheses. Take half of the coefficient of x (which is 10) and square it (10/2 = 5, 5^2 = 25):
y = -(x^2 + 10x + 25) - 25 + 24
y = -(x + 5)^2 - 1
The vertex of the parabola is at the point (-5, -1). Therefore, the y-value of the vertex is -1.
Given equation: y = -x^2 - 10x + 24
To convert this into vertex form, we need to complete the square. First, factor out the coefficient of x^2:
y = -(x^2 + 10x) + 24
Now, complete the square for the expression inside the parentheses. Take half of the coefficient of x (which is 10) and square it (10/2 = 5, 5^2 = 25):
y = -(x^2 + 10x + 25) - 25 + 24
y = -(x + 5)^2 - 1
The vertex of the parabola is at the point (-5, -1). Therefore, the y-value of the vertex is -1.