Topics
8. Solving Quadratic Equations
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United States of AmericaTennessee
Algebra 1

8.01 Solving quadratic equations using graphs and tables

Lesson
Practice
Adaptive
Worksheet

Interactive practice questions

A graph of the parabola $y=x^2+3x-10$y=x2+3x−10 is shown below.

Does the equation $x^2+3x-10=0$x2+3x−10=0 have real or non-real solutions?

Loading Graph...

Real

A

Non-real

B
Easy
< 1min

A graph of the parabola $y=-x^2+4x+4$y=−x2+4x+4 is shown below.

Does the equation $-x^2+4x+4=0$−x2+4x+4=0 have real or non-real solutions?

Easy
< 1min

A graph of the parabola $y=x^2-6x+15$y=x2−6x+15 is shown below.

Does the equation $x^2-6x+15=0$x2−6x+15=0 have real or non-real solutions?

Easy
< 1min

A table of values for the quadratic $y=x^2+7x+12$y=x2+7x+12 is shown below.

Easy
< 1min
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Outcomes

A1.N.Q.A.1

Use units as a way to understand real-world problems.*

A1.N.Q.A.1.A

Choose and interpret the scale and the origin in graphs and data displays.*

A1.A.CED.A.1

Create equations and inequalities in one variable and use them to solve problems in a real-world context.*

A1.A.CED.A.2

Create equations in two variables to represent relationships between quantities and use them to solve problems in a real-world context. Graph equations with two variables on coordinate axes with labels and scales, and use the graphs to make predictions.*

A1.A.CED.A.3

Create individual and systems of equations and/or inequalities to represent constraints in a contextual situation, and interpret solutions as viable or non-viable.*

A1.A.REI.B.3

Solve quadratic equations and inequalities in one variable.

A1.A.REI.B.3.A

Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, knowing and applying the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when a quadratic equation has solutions that are not real numbers.

A1.A.REI.D.5

Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

A1.A.REI.D.6

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x). Find approximate solutions by graphing the functions or making a table of values, using technology when appropriate.*

A1.MP2

Reason abstractly and quantitatively.

A1.MP3

Construct viable arguments and critique the reasoning of others.

A1.MP4

Model with mathematics.

A1.MP5

Use appropriate tools strategically.

A1.MP6

Attend to precision.

A1.MP7

Look for and make use of structure.

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