Free Printable Intro to Quadratics Day 3

1.

Simplify.

$\sqrt[]{36x^3}$

2.

Simplify.

$-\sqrt[]{\frac{21}{81}}$

3.

WRITING How can you use a graph to find the number of solutions of a quadratic equation?

The number of solutions is the number of (a) of the graph of the related equation.

Choose from the below words

x-intercepts

y-intercepts

maximums

minimums

4.

Describe the number of solutions a quadratic equation has.

Match the following.

a)

Two x-intercepts

1.

2 solutions (roots, zeroes)

b)

One x-intercept

2.

1 solution (root, zero)

c)

0 x-intercepts

3.

No real solutions

(root, zero)

5.

How are solutions, roots, x -intercepts, and zeros related?

a)

The solutions are the y -values that correspond to the roots, x -intercepts, and zeros of an equation.

b)

The solutions are the roots, and are the y -values that correspond to the x -intercepts and the zeros of an equation.

c)

There are two roots or zeros for every x -intercept or solution of an equation.

d)

The solutions are the same as the roots of the equation and are the same as the x -intercepts or zeros of the related equation.

6.

Write $4x^2=12$ in standard form.

7.

Write $2x-x^2=1$ in standard form.

8.

THOUGHT PROVOKING

How many different parabolas have −2 and 2 as x-intercepts?

a)

Infinitely Many

b)

1

c)

2

d)

None

e)

Cannot Be Determined Given This Information

9.

MAKING AN ARGUMENT

A stream of water from a fire hose can be modeled by $y=-0.003x^2+0.58x+3$ , where x and y are measured in feet. A firefighter standing 57 feet from a building is holding the hose 3 feet above the ground. The bottom of a window of the building is 26 feet above the ground. Will the stream of water pass through the window?

a)

The stream of water will pass through the window.

b)

The stream of water will NOT pass through the window.

c)

The stream of water's capabilities are unknown to me.

d)

Not enough information to determine.

10.

REASONING Determine whether the statement is always, sometimes, or never true. Justify your answer.

The graph of $y=ax^2+c$ has two x -intercepts when a is negative.

The statement is (a) true. When "a" is negative, the graph opens (b) . So it will have two intercepts for (c) values of "c".

Choose from the below words

sometimes

down

positive

always

never

negative

up

11.

REASONING Determine whether the statement is always, sometimes, or never true. Justify your answer.

The graph of $y=ax^2+c$ has no x -intercepts when "a" and "c" have the same sign.

The statement is (a) true. When "a" and "c" are both negative, the graph opens (b) with its vertex (c) the x-axis. When "a" and "c" are both positive, the graph opens (d) with its vertex (e) the x-axis.

Choose from the below words

always

down

below

up

above

never

negative

sometimes

12.

REASONING Determine whether the statement is always, sometimes, or never true. Justify your answer.

The graph of $y=ax^2+bx+c$ has more than two x - intercepts when $a\ne0$ .

The statement is (a) true. The possible number of x-intercepts $y=ax^2+bx+c$ can have are (b) .

Choose from the below words

never

0, 1, or 2

negative

sometimes

always

positive

0 or 1

13.

Determine the vertex of the parabola:
y = 5x²- 20x + 13

a)

(5, -7)

b)

(-2, -7)

c)

(2, -7)

d)

(-7, -2)

14.

What is the vertex of the quadratic function:
y = x² - 6x + 11?

a)

(3,2)

b)

(-3,-2)

c)

(-3,2)

d)

(3,-2)

15.

Does y = -4x² have a maximum or minimum value?

a)

maximum

b)

minimum

16.

What is the formula to find the vertex of a parabola?

a)

x = -b/2

b)

x = -b

c)

x = -b / (2a)

d)

x = -b / 2

17.

The axis of symmetry line passes through which point?

a)

y-intercept

b)

any random point

c)

vertex

d)

none of these

18.

Select the answer that has a, b, and c correctly labeled:

y=-x^2+2x-9

a)

a= 1, b= 2, c= -9

b)

a= 2, b= -1, c= 9

c)

a= -9, b= 2, c= -1

d)

a= -1, b= 2, c= -9

19.

Which direction will this parabola open?

y=2x^2+8x-16

a)

upwards

b)

downwards

20.

Factor completely
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

21.

What are the green dots called?

a)

axis of symmetry

b)

vertex

c)

parabola

d)

roots or x-intercepts

22.

What is the vertex?

a)

(5,2)

b)

(2,5)

c)

(-2,5)

d)

(-5,2)

23.

What is the y intercept for the equation:
y = -8x² + 3x - 7

a)

-8

b)

3

c)

7

d)

-7

24.

What is the y-intercept of this parabola?

a)

(−1, 3)

b)

(−3, 11)

c)

(−2, 5)

d)

(0, 5)

25.

What is the square root of 196?

a)

+ 11

b)

+ 12

c)

+ 13

d)

+ 14

26.

What shape is the graph of a quadratic?

a)

Hyperbola

b)

Parabola

c)

Straight Line

d)

Circle

27.

A parabola changes direction at what point?

a)

Slope

b)

Y-intercept

c)

vertex

d)

x-intercept

28.

An axis of symmetry is...

a)

a vertical line

b)

a horizontal line

29.

An x-intercept is also called...

a)

a root

b)

a solution

30.

A positive quadratic will open....

a)

downward

b)

upward

31.

1) What type of equation is graphed ?

a)

linear

b)

quadratic

c)

exponential

d)

constant

32.

Does this quadratic show a maximum or minimum value?

a)

Maximum

b)

Minimum

33.

Given a graph, how can you find the "solutions" to a quadratic?

a)

Call a friend

b)

Plug into a calculator

c)

Solutions are where the quadratic crosses the x-axis

d)

Magic 8 Ball -_-

34.

Choose the correct values for a, b, and c.

$4x^2-5x\ =\ 9$

a)

a = 4

b)

b = 5

c)

c = 9

d)

b = -5

e)

c = -9

35.

Graph.

$y=x^2+2x-1$

Intro to Quadratics Day 3

Total questions: 35

Worksheet time: 9hrs 45mins

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