# Thread: [SOLVED] If h(a)=0 what is the value of a, graph?

1. ## [SOLVED] If h(a)=0 what is the value of a, graph?

Hi, this is on page 859 #16 on the SAT OG Book.

The figure above shows the graph of a quadratic function h whose maximum value is h (2). If h(a)=0, which of the following could be the value of a?

a)-1
b)0
c)2
d)3
e)4

2. Is it not -1 and 3?

let h (y-axis) equal to 0. Then find the two points on the x-axis...

//j0k3r

3. That is a horrible, HORRIBLE drawing.

Was that actually supplied with the question?

4. Hello, fabxx!

That is a terrible graph!
. . And not a "neat" problem either . . .

The figure below shows the graph of a quadratic function $h(x)$
whose maximum value is $h(2).$
If $h(a)=0$, which of the following could be the value of $a$?

. . $(a)\;\text{-}1 \qquad (b)\;0 \qquad (c)\;2\qquad (d)\;3 \qquad (e)\;4$
Code:
             |
|    *
| *  :  *
*    :    *
*|    :     *
|    :
---*-+----+------*---
|    2
|
*  |            *
|
The quadratic function is a down-opening parabola.
Its maximum (vertex) is at: .(2, h(2))

If $h(a) = 0$, we are seeking the x-intercepts of the graph.
One is to the left of the origin (negative)
. . the other is to the right of $x = 2.$

We know that the two intercepts are symmetric
. . about the axis of symmetry, $x = 2.$

Since the left intercept is negative, it is more than 2 units to the left of $x = 2.$

Then the right intercept is more than 2 units to the right of $x = 2.$
. . Hence: . $a > 4$

Among the given choices, the only one is: . $a = \text{-}1$ . . . answer (a)