Free Printable Characteristics of Quadratics and their Graphs

1.

State the vertex of the graph whose function is $f\left(x\right)=\left(x-4\right)^2+8$

a)

(4,8)

b)

(4, -8)

c)

(-4, 8)

d)

(-4, -8)

2.

State the vertex $f\left(x\right)=\left(x+2\right)^2-6\$

a)

(2, 6)

b)

(-2, -6)

c)

(-2, 6)

d)

(2, -6)

3.

What is the domain of:

y=-2x^{2\ }+5x-9

a)

$x\le4$

b)

$y<-9$

c)

$x=All\ real\ numbers$

d)

$y=All\ real\ numbers$

4.

What is the minimum value? $y=\left(x-2\right)^2-13$

a)

2

b)

-2

c)

13

d)

-13

5.

State the axis of symmetry $f\left(x\right)=3\left(x+5\right)\left(x-2\right)$

a)

$x=-1.5\ or\ x=-\frac{3}{2}$

b)

$y=-1.5\ or\ y=-\frac{3}{2}$

c)

$x=1.5\ or\ x=\frac{3}{2}$

d)

$y=1.5\ or\ y=\frac{3}{2}$

6.

What is the vertex of $f\left(x\right)=\ \left(x+1\right)\left(x+3\right)$

a)

$\left(2,\ 8\right)$

b)

$\left(2,\ 15\right)$

c)

$\left(-2,\ 1\right)$

d)

$\left(-2,\ -1\right)$

7.

State the range

a)

$y<-7$

b)

$y\le-7$

c)

$y>-7$

d)

$y\ge-7$

8.

State the axis of symmetry $f\left(x\right)=2x^2-x+4$

a)

$x=-\frac{1}{4}$

b)

$x=\frac{1}{4}$

c)

$y=\frac{1}{4}$

d)

$x=\frac{1}{2}$

9.

State the interval on which the function is increasing

a)

$x<0$

b)

$x>0$

c)

$y<0$

d)

$y>0$

10.

State the interval on which the function is decreasing

a)

$x\le-2$

b)

$x\ge-2$

c)

$x<-2$

d)

$x>-2$

11.

Does the following graph of the quadratic have a maximum or minimum: $y=\left(x-1\right)\left(x-6\right)$

a)

maximum

b)

minimum

c)

neither

d)

both

12.

Does the following graph of the quadratic have a maximum or minimum: $y=-3\left(x+4\right)^2+7$

a)

maximum

b)

minimum

c)

neither

d)

both

13.

State the axis of symmetry $y=-3\left(x+4\right)^2+7$

a)

$x=4$

b)

$y=4$

c)

$x=-4$

d)

$y=-4$

14.

State the y-intercept: $y=2x^2+46x-2$

a)

$\left(0,\ 2\right)$

b)

$\left(0,\ 46\right)$

c)

$\left(0,\ -2\right)$

d)

$\left(0,\ -46\right)$

Characteristics of Quadratics and their Graphs

Total questions: 14

Worksheet time: 7mins

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