Identify the vertex of y=4(x−25)2−61 .(1 point) Responses (4,−25) left parenthesis 4 comma negative 25 right parenthesis (−100,−61) left parenthesis negative 100 comma negative 61 right parenthesis (−25,−61) left parenthesis negative 25 comma negative 61 right parenthesis (25,−61)
First, let's simplify the equation to eliminate the unnecessary components to identify the vertex.
y = 4(x - 25)^2 - 61.
The vertex form of a parabolic equation is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
Comparing the given equation with the vertex form, we can see that h = 25 and k = -61.
Therefore, the vertex is (25, -61).
So, the correct answer is (25, -61).
To identify the vertex of the quadratic function y=4(x−25)2−61, we can use the vertex form of a quadratic equation: y=a(x-h)2+k, where (h, k) represents the coordinates of the vertex.
In this case, the equation is y=4(x−25)2−61, so we can identify that the vertex form is y=4(x-25)2-61. The coefficient "a" is 4, which gives us a positive value. This means the parabola opens upwards.
Next, we can compare this equation to the vertex form. We have (h, k) as the coordinates of the vertex. By comparing, we can see that h = 25 and k = -61.
Therefore, the vertex of the given function y=4(x−25)2−61 is (25, -61).
To identify the vertex of the quadratic function, we need to find the values of x and y that make the function reach its highest or lowest point. The vertex form of a quadratic function is given by y = a(x - h)^2 + k, where the vertex is at the point (h, k).
Comparing this with the given function y = 4(x - 25)^2 - 61, we can see that 4 is the value of a, -25 is the value of h, and -61 is the value of k.
Therefore, the vertex of the function y = 4(x - 25)^2 - 61 is (25, -61).