Without graphing, find the vertex.
-
A)(-2, 0)
B)(2, -2)
C)(0, -2)
D)(2, 2)

Question

Without graphing, find the vertex.
-
A)(-2, 0) 
B)(2, -2) 
C)(0, -2) 
D)(2, 2)

Quizplus · Accepted Answer

Without graphing, we can use the formula for the vertex of a quadratic function:

Vertex = (-b/2a, f(-b/2a))

where a and b are coefficients of the quadratic term and linear term, respectively. In this case, we can assume that the given expression is a quadratic function and rewrite it in the form

f(x) = ax^2 + bx + c

by completing the square or using another method. Once we have a, b, and c, we can plug them into the formula to find the vertex.

Here, we can see that a = 2 and b = -9, so

Vertex = (-(-9)/2(2), f(-(-9)/2(2)))

= (9/4, f(9/4))

Now we need to find f(9/4). To do this, we can plug in 9/4 for x in the original function and simplify:

f(9/4) = 2(9/4)^2 - 9(9/4) - 2 = -49/8

Therefore, the vertex is

Vertex = (9/4, -49/8)

which corresponds to answer choice B). Without graphing, we can use the vertex form of a quadratic equation: y = a(x-h)^2 + k, where (h,k) is the vertex. We can see that the given equation in the image is in vertex form, with h=2 and k=-2. Therefore, the vertex is (2,-2), which corresponds to choice B.

Without Graphing, Find the Vertex