Free Practice Quiz Question List

07/14 7. Quadratic Functions and Equations Online Quiz Questions

Use this free practice quiz with 20 questions to review 07/14 7. Quadratic Functions and Equations, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

For the quadratic function $f(x)=-3x^2+2x+1$ , which description of its graph is correct?

A
It opens upward and is wider than $y=x^2$ .
B
It opens downward and is narrower than $y=x^2$ .
C
It opens upward and is narrower than $y=x^2$ .
D
It opens downward and is wider than $y=x^2$ .

Choose one

1 point

For $f(x)=2(x+2)^2+7$ , which statement identifies the vertex and axis of symmetry?

A
The vertex is $(2,7)$ , and the axis is $x=2$ .
B
The vertex is $(-2,-7)$ , and the axis is $x=-2$ .
C
The vertex is $(-2,7)$ , and the axis is $x=-2$ .
D
The vertex is $(7,-2)$ , and the axis is $x=7$ .

Choose one

1 point

How many real solutions does $x^2+6x+9=0$ have?

A
Two distinct real solutions
B
Two complex solutions and no real solutions
C
One real solution and one nonreal solution
D
One repeated real solution

Choose all

1 point

Which two statements correctly describe a quadratic function in factored form $f(x)=a(x-r_1)(x-r_2)$ ? Select all correct choices.

A
For $f(x)=a(x-r_1)(x-r_2)$ , the zeros are $x=r_1$ and $x=r_2$ .
B
The y-intercept is always $(0,r_1+r_2)$ .
C
The x-intercepts correspond to the values that make a factor equal to zero.
D
The axis of symmetry is always $x=a$ .

Choose all

1 point

Which two statements give sound guidance for choosing a method to solve a quadratic equation? Select all correct choices.

A
Use factoring when the quadratic factors easily.
B
Use completing the square only when the leading coefficient is negative.
C
Use the square-root property for every quadratic equation.
D
Use the quadratic formula when a dependable method is needed for any quadratic equation.

True or false

1 point

True or false: For a quadratic function in standard form $f(x)=ax^2+bx+c$ , the y-intercept is $(0,c)$ .

A
True
B
False

True or false

1 point

True or false: In a projectile model, the positive solution to $h(t)=0$ represents the time when the object reaches the ground.

A
True
B
False

Written response

1 point

Find the x-coordinate of the vertex of $f(x)=3x^2-12x+7$ .

Fill in the blank

1 point

Solve $x^2-9x+20=0$ by factoring. The two solutions are $x=$ and $x=$ .

Fill in the blank

1 point

Complete the square in $x^2+10x$ . Add to obtain the perfect-square expression .

Open ended

1 point

Solve $x^2+4x-1=0$ by completing the square. Show the key steps and give both exact solutions.

Choose one

1 point

A rectangle has width $x$ , length $x+5$ , and area 84 square units. What is its width?

A
The width is 12 units.
B
The width is 7 units.
C
The width is $-12$ units.
D
The width is 84 units.

Choose one

1 point

What can be concluded about the graph of $f(x)=-3x^2+7x-1$ ?

A
The parabola opens upward and has a minimum.
B
The parabola opens downward and has a maximum.
C
The parabola opens upward and has a maximum.
D
The parabola opens downward and has a minimum.

Choose one

1 point

What is the vertex of $f(x)=4(x+2)^2-7$ ?

A
$(2,-7)$
B
$(-2,-7)$
C
$(-2,7)$
D
$(4,-7)$

Choose one

1 point

What is the axis of symmetry of $f(x)=x^2-8x+3$ ?

A
$x=-8$
B
$x=2$
C
$x=4$
D
$x=8$

Choose one

1 point

If the discriminant of a quadratic equation is $0$ , how many real solutions does the equation have?

A
Two distinct real solutions
B
One repeated real solution
C
No real solutions and one complex solution
D
Two different complex solutions

True or false

1 point

True or false: If $uv=0$ , then $u=0$ or $v=0$ .

A
True
B
False

Written response

1 point

A ball is launched from ground level with height $h(t)=-16t^2+64t$ , where $t$ is measured in seconds and $h(t)$ in feet. What is the ball's maximum height, in feet?

Written response

1 point

What is the name of the expression $b^2-4ac$ in the quadratic formula?

Written response

1 point

A simplified profit model is $P(x)=-x^2+10x-21$ . At which smaller positive value of $x$ does the profit equal zero?