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

Question

Quizplus · Accepted Answer

This is the vertex form, where the vertex is (3,4) and the coefficient a is positive, indicating a minimum. To find the intercepts, set y to 0 and solve for x: 
0 = 2(x - 3)^2 + 4
-4 = 2(x - 3)^2
-2 = (x - 3)^2
x = 3 ± √2. These are the x-intercepts. To find the y-intercept, set x to 0: 
y = 2(0 - 3)^2 + 4 = 22. Therefore, the intercepts are x = 3 ± √2 and y = 22. The range is [4, ∞), since the minimum value is 4 and the function increases from there. 
Answer: B) Vertex
 The vertex is (3,4), as given by the vertex form. 
Answer: C) Maximum or minimum
 The coefficient a is positive, indicating a minimum. Therefore, the vertex is the minimum value, which is 4. 
Answer: D) Range
 The range is [4, ∞), as explained above.

Find the Vertex Form for the Quadratic Function