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8.01 Solve quadratics using graphs and tables

Adaptive
Worksheet

Interactive practice questions

Consider the graph of $y=x^2-2x-15$y=x22x15.

Loading Graph...

Which of the following are solutions to the equation $x^2-2x-15=0$x22x15=0?

Select all the correct options.

$x=-15$x=15

A

$x=-3$x=3

B

There are no solutions.

C

$x=5$x=5

D
Medium
< 1min

Consider the graph of $y=-2x^2-4x-3$y=2x24x3.

Medium
< 1min

Consider the graph of the function $f\left(x\right)=1.09x^2-5.51x-9.28$f(x)=1.09x25.51x9.28.

Medium
< 1min

By graphing $y=3x^2-2x-40$y=3x22x40 and $y=-x^2+2x+8$y=x2+2x+8 on a graphing calculator or otherwise, find the solutions of the equation $3x^2-2x-40=-x^2+2x+8$3x22x40=x2+2x+8. Write both solutions on the same line separated by a comma.

Medium
2min
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Outcomes

A.EI.3

The student will represent, solve, and interpret the solution to a quadratic equation in one variable.

A.EI.3a

Solve a quadratic equation in one variable over the set of real numbers with rational or irrational solutions, including those that can be used to solve contextual problems.

A.EI.3b

Determine and justify if a quadratic equation in one variable has no real solutions, one real solution, or two real solutions.

A.EI.3c

Verify possible solution(s) to a quadratic equation in one variable algebraically, graphically, and with technology to justify the reasonableness of answer(s). Explain the solution method and interpret solutions for problems given in context.

A.F.2

The student will investigate, analyze, and compare characteristics of functions, including quadratic and exponential functions, and model quadratic and exponential relationships.

A.F.2c

Graph a quadratic function, f(x), in two variables using a variety of strategies, including transformations f(x) + k and kf(x), where k is limited to rational values.

A.F.2g

For any value, x, in the domain of f, determine f(x) of a quadratic or exponential function. Determine x given any value f(x) in the range of f of a quadratic function. Explain the meaning of x and f(x) in context.

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