Quadratic Formula

​Fall Interim Review
4% of all the students got this question correct.

Multiple Choice

A youth orchestra is selling advertising space in their music programs to raise money. The orchestra has a goal to raise $2,500 or more by selling small and large-sized advertisements to local businesses. The graph of the inequality shown below represents possible combinations of each size of advertisement that could be sold to meet or exceed the fundraising goal. In the graph, represents the number of small-sized advertisements sold and represents the number of large-sized advertisements sold.

• $$50x+20y\le2500$$

• $$50x+20y\ge2500$$

• $$50x+125y\ge2500$$

• $$50x+125y\ \le\ 2500$$

​Get x-intercept by setting y=0

Get y-intercept by setting x=0

You had to type in the inequality using "$2500 or more" which is >

​Fall Interim Review
6% of all the students got this question correct.

Multiple Choice

The graph of y = x + 1 is shown on the coordinate plane. Graph the equation $$y=\frac{1}{3}x-3$$ on the same coordinate plane below. Then graph the point that represents the solution to this system of linear equations.

​You had to use the point button for the solution.

​Fall Interim Review
10% of all the students got this question correct.

Multiple Select

A bride and groom both invited guests to their wedding.  The bride invited twice as many women as the groom did, and the groom invited twice as many men as the bride did.  If the bride invited 135 guests and the groom invited 105 guests, which of these is the number of men or the number of women that either the bride or groom invited?  Select three that apply.

• 25

• 50

• 100

• 105

• 110

​So, 55 women were invited and 25 men were invited by the bride and groom. Then you can use that information to find the exact number invited by the bride and groom.

​the bride invited 2w + m = 135 if there were 55 women that means there were 110 women because we know the bride invited "twice" the women compared to the groom.

​the groom invited w + 2m = 105 if there were 25 men that means there were 50 men because we know the groom invited "twice" the men compared to the bride.

​Fall Interim Review
12% of all the students got this question correct.

Multiple Select

Choose all of the equations that have "No Solution."

• $$2\left(x+1\right)=3+2x-1$$

• $$9x=2x$$

• $$\left(x+1\right)-\left(x-2\right)=11$$

• $$2+3x=3x-5$$

• $$2+x=3$$

​The x's cancel and 3 does not equal 11.

​The 3x's cancel and 2 does not equal -5

​The x's cancel and 3 does not equal 11.

​The 3x's cancel and 2 does not equal -5

​

​The x's cancel and 3 does not equal 11.

​The 3x's cancel and 2 does not equal -5

​Fall Interim Review
12% of all the students got this question correct.

Multiple Choice

Lauren plans to graph the function described by the equation $$3x+4y=10$$ In her first step to graph the function, Lauren needs to determine the x-intercept. What is the ordered pair for the x-intercept?

• $$\left(0,\ 2\right)$$

• $$\left(0,\frac{5}{2}\right)$$

• $$\left(3,\ 0\right)$$

• $$\left(\frac{10}{3},\ 0\right)$$

​Also, x-intercept is C/A

​Fall Interim Review
13% of all the students got this question correct.

Multiple Choice

John walks at a constant speed.  The distance, d, John walks is equal to d = s × t, where s is the speed in miles per hour at which he walks and t is the amount of time in hours he walks for.

Enter an equation that can be used to find the speed, s, at which John walks.

• $$s=\frac{d}{t}$$

• $$s=d\times t$$

• $$s=t\times d$$

• $$s=\frac{t}{d}$$

​Fall Interim Review
15% of all the students got this question correct.

Multiple Choice

How does adding a constant to the parent function ( y = x ) affect the graph of the function?

• It changes the slope.

• It translates the graph.

• It reflects the graph.

• It compresses the graph.

​Fall Interim Review
15% of all the students got this question correct.

Multiple Choice

The flowchart below details the process of finding the equation of a line parallel to the line $$y=-2x+4$$ and passing through the point (-3, 4). Fill in the empty boxes in the flowchart with statements describing how to determine the slope and y-intercept of the parallel line.  Which equation is parallel and passes through the point?

• $$y=-2x-2$$

• $$y=2x-4$$

• $$y=\frac{1}{2}x+4$$

• $$y=-2x-3$$

​Fall Interim Review
17% of all the students got this question correct.

Multiple Choice

Assume that $$f\left(x\right)=2x+4$$ . The function $$f\left(x\right)+k$$ , where k is a constant, is represented in the graph. What effect did adding k have on the graph of f(x)?

• It shifted 4 units up

• It shifted 3 units left

• It shifted 1 unit right

• It shifted 6 units down

​Fall Interim Review
21% of all the students got this question correct.

Multiple Choice

Which equation rewriting process is shown?

• Slope Intercept to Standard Form to Point Slope Form

• Point Slope to Slope Intercept to Standard Form

• Standard Form to Point Slope Form to Slope Intercept Form

• Slope Intercept to Point Slope to Standard Form

​Fall Interim Review
24% of all the students got this question correct.

Multiple Choice

Complete the table, and graph the linear equation. Choose the table that represent the pairs of coordinates when graphing $$3x-y=1$$ .

That's it for review! Let's talk about the quadratic formula!

Multiple Choice

What would the equation be the a, b coefficients, and the constant c? $$3p^2-2p+19\ =\ 24$$

• a= 3, b= -2, c= 19

• a= 19, b= 3, c= -2

• a= 3, b= -2, c= -5

• a= 3, b= -2, c= 43

Multiple Choice

Which correctly shows the proper use of the quadratic formula for the equation? $$3p^2-2p-5$$

• $$\frac{-3\pm\sqrt[]{\left(-5\right)^2-4\left(3\right)\left(-2\right)}}{2\left(-2\right)}$$

• $$\frac{-2\pm\sqrt[]{\left(-2\right)^2-4\left(3\right)\left(-5\right)}}{2\left(3\right)}$$

• $$\frac{-\left(-2\right)\pm\sqrt[]{\left(3\right)^2-4\left(3\right)\left(-2\right)}}{2\left(-5\right)}$$

• $$\frac{-\left(-2\right)\pm\sqrt[]{\left(-2\right)^2-4\left(3\right)\left(-5\right)}}{2\left(3\right)}$$

Multiple Select

Choose all of the solutions for the equation $$3p^2-2p-5$$ .

• $$-1$$

• $$\frac{1}{3}$$

• $$1\frac{2}{3}$$

• $$1$$

• $$1\frac{6}{7}$$

Multiple Select

What are the solutions represented in the graph?

• 1

• -3

• -5

• -1

• 3

Open Ended

What should be done in order to determine a, b, and c of the quadratic equation? $$2n^2=10n+5$$

Multiple Select

Choose all of the expressions with a discriminant of 213? $$\frac{-b\pm\sqrt[]{discri\min ant}}{2a}$$

• $$\frac{-129\pm\sqrt[]{213}}{17}$$

• $$\frac{213\pm\sqrt[]{17}}{129}$$

• $$\frac{-17\pm\sqrt[]{213}}{129}$$

• $$\frac{17\pm\sqrt[]{129}}{213}$$

• $$\frac{-1\pm\sqrt[]{213}}{129}$$

Open Ended

How do you calculate the discriminant?

Multiple Choice

What is the discriminant for the former equation after setting it equal to zero? $$0=-2n^2+10n+5$$ (note: the discriminant is b squared minus 4 times a times c)

• 60

• 140

• 180

• 10

Multiple Choice

What are the solutions to the equation? $$-8r^2-9r-1=-9$$

• $$-\frac{9\pm\sqrt[]{337}}{16}$$

• $$-\frac{5\pm2\ \sqrt[]{52}}{18}$$

• $$-\frac{5\pm\sqrt[]{176}}{18}$$

• $$-\frac{2\pm\sqrt[]{337}}{9}$$