Question
what is the y-value of the vertex? y = -x^2 - 10x + 24
Answers
GPT 3.5
To find the y-value of the vertex of the quadratic equation y = -x^2 - 10x + 24, we first need to determine the x-coordinate of the vertex.
The x-coordinate of the vertex of a quadratic equation in the form y = ax^2 + bx + c can be calculated using the formula x = -b/(2a).
In this case, a = -1, b = -10, and c = 24. Plugging these values into the formula, we have:
x = -(-10) / (2*(-1)) = 10 / -2 = -5
Now that we have found the x-coordinate of the vertex to be -5, we can substitute this value back into the original equation to find the y-value. Plugging x = -5 into y = -x^2 - 10x + 24, we get:
y = -(-5)^2 - 10(-5) + 24
y = -25 + 50 + 24
y = 49
Therefore, the y-value of the vertex is 49.
The x-coordinate of the vertex of a quadratic equation in the form y = ax^2 + bx + c can be calculated using the formula x = -b/(2a).
In this case, a = -1, b = -10, and c = 24. Plugging these values into the formula, we have:
x = -(-10) / (2*(-1)) = 10 / -2 = -5
Now that we have found the x-coordinate of the vertex to be -5, we can substitute this value back into the original equation to find the y-value. Plugging x = -5 into y = -x^2 - 10x + 24, we get:
y = -(-5)^2 - 10(-5) + 24
y = -25 + 50 + 24
y = 49
Therefore, the y-value of the vertex is 49.