﻿ Graphing Quadratic Functions Worksheet | Problems & Solutions

• Page 1
1.
Katie says without drawing the graph of $y$ = - 2$x$2 + 4, we can find out if its vertex is above or below the point (0, 0). Is she correct?
 a. No b. Yes

#### Solution:

Yes, Katie is correct.
It is possible to predict without drawing the graph of y = - 2x2 + 4, if its vertex would be above or below the point (0, 0).

For y = - 2x2 + 4, a = - 2, b = 0 and c = 4.
[Compare with y = ax2 + bx + c.]

Consider y = ax2 + c:
If c is positive, then the vertex of the graph of y = ax2 + c will be c units above the point (0, 0).
If c is negative, then the vertex of the graph of y = ax2 + c will be c units below the point (0, 0).

Here we have c = 4. So, the vertex of the graph of y = - 2x2 + 4 will be 4 units above the point (0, 0).

2.
Identify the list that shows all the possible rational roots of the equation 4$x$13 + 4$x$7 + 2$x$ + 5 = 0.
 a. ± $\frac{1}{2}$, ± $\frac{1}{4}$, ± $\frac{5}{2}$, ± $\frac{5}{4}$ b. ± 1, ± $\frac{1}{2}$, ± $\frac{1}{4}$ , ± 5 c. ± 1, ± $\frac{1}{2}$, ± $\frac{1}{4}$, ± 5, ± $\frac{5}{2}$, ± $\frac{5}{4}$ d. ± 1, ± 5

#### Solution:

Constant term = 5

Factors of 5 are ± 1 and ± 5.

Factors of 4 are ± 1, ± 2, and 4.

Rational root = an integral factor of the constantan integral factor of the leading coefficient = ± 1, ± 12, ± 14, ± 5, ± 52, ± 54

3.
At how many points does the graph of $y$ = $x$2 - 3$x$ - 40 intersect the $x$-axis?
 a. one b. two c. three d. zero

#### Solution:

The graph of y = x2 - 3x - 40 intersect the x-axis at y = 0

For y = 0, x = 8 and - 5
[Substitute y = 0 in y = x2 - 3x - 40 and solve for x.]

Therefore, the points at which the graph intersect the x-axis are (8, 0) and (- 5, 0).

So, the graph intersects the x-axis at two points.

4.
At how many points does the graph of $y$ = $x$2 - 2$x$ + 1 intersect the $x$-axis?
 a. zero b. two c. cannot be determined d. one

5.
At how many points does the graph of $y$ = $x$2 + 2$x$ + 3 intersect the $x$-axis?
 a. cannot be determined b. two c. one d. zero

6.
At how many points does the graph of $y$ = $x$2 - 12$x$ + 36 intersect the $x$-axis?
 a. cannot be determined b. zero c. two d. one

7.
At how many points does the graph of $y$ = $x$2 - 4$x$ - 5 intersect the $x$-axis?
 a. two b. cannot be determined c. one d. zero

8.
At how many points does the graph of $y$ = 2$x$2 - 5$x$ - 25 intersect the $x$-axis?
 a. zero b. two c. cannot be determined d. one

9.
At how many points does the graph of $y$ = $x$2 - 3$x$ - 4 intersect the $x$-axis?
 a. zero b. one c. two d. cannot be determined

What is the effect of the constant factor on the slope of the functions $y$1 = 5$x$2 - 2$x$ + 11 and $y$2 = $x$2 - $\frac{2}{5x}$ + $\frac{11}{5}$?