Identify the vertex of y=4(x−25)2−61
.(1 point)
Responses
(25,−61)
left parenthesis 25 comma negative 61 right parenthesis
(−25,−61)
left parenthesis negative 25 comma negative 61 right parenthesis
(−100,−61)
left parenthesis negative 100 comma negative 61 right parenthesis
(4,−25)
None of the given options are the correct vertex.
The vertex of the quadratic function y = 4(x−25)2−61 is obtained by finding the values of x and y that make the expression inside the parentheses (x−25) equal to 0.
Set x−25 = 0 and solve for x:
x−25 = 0
x = 25
Substitute x = 25 into the equation to find y:
y = 4(25−25)2−61
y = 4(0)2−61
y = 0−61
y = -61
Therefore, the correct vertex is (25, -61).
To identify the vertex of the equation y=4(x-25)^2-61, we can compare it to the equation y=a(x-h)^2+k, where (h,k) represents the vertex of the parabola.
In this equation, h = 25 and k = -61. Therefore, the vertex is (25, -61).
To identify the vertex of the quadratic function y=4(x−25)²−61, we can use the vertex formula. The vertex formula for a quadratic function in the form y=a(x−h)²+k is (h, k), where (h, k) represents the coordinates of the vertex.
In this case, the equation is y=4(x−25)²−61. Comparing this to the vertex formula, we can see that h=25 and k=-61. Therefore, the coordinates of the vertex are (25, -61).
So, the correct answer is:
(25, -61)
or
left parenthesis 25, comma negative 61 right parenthesis.