How could you use this kind of thinking to solve: $$x^2 - x - 12 = 0$$ ?

By factoring the quadratic equation

How does solving the equation relate to the graph and the x-intercepts?

Solving the equation determines the x-intercepts of the graph.

Solving the equation gives the slope of the graph.

Solving the equation provides the y-intercept of the graph.

Solving the equation gives the maximum point of the graph.

Starting with f(x) in vertex form, which of the following steps correctly solves the equation f(x) = 0 using inverse operations?

Subtract the constant term from both sides, then take the square root.

Add the constant term to both sides, then take the square root.

Multiply both sides by the leading coefficient, then take the square root.

Divide both sides by the leading coefficient, then take the square root.

g. How do your solutions compare with your estimates of the x-intercepts and the distance from the line of symmetry and the x-intercepts?

The solutions are slightly different from the estimates.

The solutions are exactly the same as the estimates.

The solutions are completely different from the estimates.

The solutions cannot be compared to the estimates.

What is the distance from line of symmetry to an x-intercept?

The distance is half the distance between the x-intercepts.

The distance is equal to the x-coordinate of the vertex.

The distance is the same as the y-coordinate of the vertex.

Find two methods for solving this equation graphically: $$3x^2 + 3x - 5 = -x + 7$$ .

Plotting both sides of the equation as separate functions and finding their intersection points.

Using a graphing calculator to find the roots of the equation.

Transforming the equation into a linear form and plotting it.

Using a table of values to approximate the solution.

{"query":"Complete the procedure to solve the quadratic equation by factoring. Fill in the blanks: is ______.","answer":0,"options":["factored as (x + 6)(x - 2) = 0."],"type":"BLANK","aiCreateMeta":{"sourceImage":"https://quizizz-static.s3-accelerate.amazonaws.com/_media/uploadedFiles/8987db5f-cb02-455e-a1d9-f51a433be79b-v2","hasDiagram":false}}

factored as (x + 6)(x - 2) = 0.

factored as (x + 3)(x - 4) = 0.

factored as (x + 2)(x - 6) = 0.

factored as (x + 1)(x - 12) = 0.

Which of the following methods are learned for solving quadratic equations as mentioned in the lesson summary?

Factoring, Completing the Square, Quadratic Formula

Graphing, Substitution, Elimination

Integration, Differentiation, Limits

Matrix Multiplication, Determinants, Eigenvalues

Find the features for the function represented in the graph. Intervals of Increase: ______, Intervals of Decrease: ______, Maximum: ______, Minimum: ______, Domain: ______, Range: ______.

The question has a diagram associated with it. The diagram has been stored separately.

The function is linear with no maximum or minimum.

The function is quadratic with a single maximum point.

The function is constant with no intervals of increase or decrease.

Imagine one of the big blocks and the extra smaller blocks. What goes into each of the sections? You’ve been given a start below. Try filling in the other sections. Now that you have filled in the small square, what expression do you need to subtract from c? Don’t forget that you have a big blocks and the diagram shows just one of them. Complete the diagram including the lengths of the sides.

The question is asking for the contents of the sections in a diagram involving big and small blocks, what expression to subtract from c, and to complete the diagram with lengths of the sides.

The question is asking for the number of blocks needed to fill a given area and the total cost of the blocks.

The question is asking for the volume of the blocks and the material used to make them.

The question is asking for the weight of the blocks and the method to transport them.

4. Write and solve the equation for f(x) = 0 just using inverse operations and some fancy algebra.

Use inverse operations to isolate x.

Graph the function and find the x-intercepts.

Substitute x with a known value.

Solve the quadratic equation: $$x^2 - 5x - 5 = 0$$ .

The solutions to the equation are: $x = \frac{5 \pm \sqrt{25 + 20}}{2} = \frac{5 \pm \sqrt{45}}{2} = \frac{5 \pm 3\sqrt{5}}{2}$.

The solutions to the equation are: $x = \frac{5 \pm \sqrt{25 - 20}}{2} = \frac{5 \pm \sqrt{5}}{2}$.

The solutions to the equation are: $x = \frac{5 \pm \sqrt{25 + 10}}{2} = \frac{5 \pm \sqrt{35}}{2}$.

The solutions to the equation are: $x = \frac{5 \pm \sqrt{25 - 10}}{2} = \frac{5 \pm \sqrt{15}}{2}$.

Why do the solutions from the quadratic formula contain a “±”?

Because it represents the two possible values for the square root.

Because it indicates the presence of complex numbers.

Because it shows the equation has no real solutions.

Because it simplifies the calculation process.

Is it possible to have only one solution to a quadratic equation? What would that mean about the associated function?

Yes, it means the function has a double root and the vertex touches the x-axis.

No, a quadratic equation always has two distinct solutions.

Yes, it means the function has no real roots and the graph is above the x-axis.

No, it means the function is not a quadratic.

What does it mean if the number inside the root of a solution turns out to be negative?

The solution is undefined in the real number system.

The solution is a positive real number.

The solution is a negative real number.

How do you find x-intercepts for a given equation?

Find the derivative and set it to zero

Integrate the equation and solve for x

Given: $$x^2 + 4x - 8 = 0$$ . Can this equation be solved by factoring? How can you tell?

No, because the equation cannot be expressed as a product of two binomials.

Yes, because the equation can be expressed as a product of two binomials.

Yes, because the equation has a perfect square trinomial.

No, because the equation has no real roots.

Unit 3, Lesson 1

Authored by Melissa Smith

Mathematics

10th Grade

CCSS covered

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76 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What are the solution(s) to the quadratic equation x^2 = 9?

x = 3

x = -3

x = 3 and x = -3

x = 0

Tags

CCSS.HSA-REI.B.4B

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the shape of the graph of the function f(x) = x^2?

Line

Parabola

Circle

Ellipse

Tags

CCSS.HSF-IF.C.7A

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

For what values of x does f(x) = 9?

x = 1

x = 2

x = 3

x = 4

Tags

CCSS.HSF.IF.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What are the solutions to the equation (x - 1)^2 = 4?

x = 1

x = 3 and x = -1

x = 5 and x = -3

x = 3 and x = -3

Tags

CCSS.HSA-REI.B.4B

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Given the equation (x - 1)^2 = 4: What are the x-values where f(x) = 4 for the function f(x) = (x - 1)^2?

x = 1

x = 3 and x = -1

x = 3 and x = -3

x = 5 and x = -3

Tags

CCSS.8.EE.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Given the equation: -x^2 - 6x - 7 = 1. What are the solution points where f(x) = 1?

x = -3 and x = -1

x = -4 and x = -2

x = -5 and x = -1

x = -7 and x = 1

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

x^2 - x - 12 = 0

x^2 + 7x + 12 = 0

x^2 - 7x + 12 = 0

x^2 + x - 12 = 0

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

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Unit 3, Lesson 1

What are the solution(s) to the quadratic equation x^2 = 9?

What is the shape of the graph of the function f(x) = x^2?

For what values of x does f(x) = 9?

What are the solutions to the equation (x - 1)^2 = 4?

Given the equation (x - 1)^2 = 4: What are the x-values where f(x) = 4 for the function f(x) = (x - 1)^2?

Given the equation: -x^2 - 6x - 7 = 1. What are the solution points where f(x) = 1?

Now you can try a few. Solve each quadratic equation by factoring.

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