Find the vertex form for the quadratic function. Then find each of the following:
(A) Intercepts
(B) Vertex
(C) Maximum or minimum
(D) Range
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Question

Quizplus · Accepted Answer

B) x-intercepts: None
y-intercept: (0,-17)
C) Vertex: (3,-5); Minimum
D) Range: y ≥ -5
Answer: B,C,D
 
For part A, we can see that the vertex form of the quadratic function is y = a(x-h)^2 + k, where (h,k) is the vertex. We have the equation in this form, so we can identify the vertex as (3,-5).

For part B, we can find the x-intercepts by setting y = 0 and solving for x. In this case, we get 2(x-3)^2 - 5 = 0, which simplifies to (x-3)^2 = 5/2. This equation does not have real solutions, so there are no x-intercepts. To find the y-intercept, we set x = 0 and solve for y. Plugging in x=0 to the vertex form equation, we get y = 2(0-3)^2 - 5 = -17. So the y-intercept is (0,-17).

For part C, we can see that the coefficient a is positive, so the parabola opens upwards and the vertex is a minimum.

For part D, we can see that the minimum value of y is -5, since the vertex is at (3,-5) and the parabola opens upwards. Therefore, the range of the function is y ≥ -5.

Find the Vertex Form for the Quadratic Function