Question

2 Which quadratic function describes the

graphed parabola with zeros at x = 1 and x = 5?
у
6
5
4
13
2
1
х
-6543
-2
-1
0
23
4 51
6
-1
- 2
ܬ ܪ ܬܢ
F f(x) = -2(x - 3)2 + 8
G f(x) = -2x2 + 12x - 10
H f(x) = -0.5(x - 3)2 + 2
J f(x) = -0.5x² – 3x - 6

Answer 1

9514 1404 393

Answer:

H f(x) = -0.5(x -3)² +2

Explanation:

The quadratic opens downward, so the leading coefficient is negative. All answer choices agree on this.

The vertex (maximum point) is (3, 2). Choices F and H are written in vertex form. Choice F has a vertex of (3, 8); choice H has a vertex of (3, 2), so is a likely candidate.

When we look at the graph 1 unit right or left of the vertex, we see that it is about 1.5, that is, 0.5 units below the vertex. This 0.5 is the magnitude of the leading coefficient, which we already know is negative. The leading coefficient of -0.5 eliminates choices F and G.

So, choice H has the correct leading coefficient and the correct vertex.

Choice J can be eliminated by looking at the value for x=0. For J, it is -6, but we see the y-intercept of the graph is -2.5. This eliminates choice J.

The only viable choice is H.