4. Quadratics

4.01 Key features of quadratic functions

4.02 Solving quadratic equations by factoring

4.03 Solving quadratic equations using square roots

Investigation: Deriving the quadratic formula

4.04 The discriminant and the quadratic formula

4.05 Graphing quadratic functions

4.06 Transformations of quadratics

4.07 Quadratics in factored form

4.08 Quadratics in vertex form

4.09 Quadratic functions and technology

4.10 Applications of quadratic functions

4.11 Comparing exponential and quadratic functions

4.12 Systems of linear and quadratic equations

United States of America UT

Math II

4.03 Solving quadratic equations using square roots

Interactive practice questions

Is $y=-2$y=−2 a solution of $5y^2+4y=-12$5y2+4y=−12?

Yes

A

No

B

Easy

< 1min

Is $x=\frac{1}{4}$x=14 a solution of $48x^2+16x-7=0$48x2+16x−7=0?

Easy

< 1min

Is $x=\frac{8}{7}$x=87 a solution of $\left(7x-2\right)^2=37$(7x−2)2=37?

Easy

< 1min

Is $x=-\frac{3}{4}$x=−34 a solution of $20x^2=3-11x$20x2=3−11x?

Easy

1min

Outcomes

II.A.CED.1

Create equations and inequalities in one variable and use them to solve problems.

II.A.CED.4

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations; extend to formulas involving squared variables.

II.A.REI.4

Solve quadratic equations in one variable.

II.A.REI.4.b

Solve quadratic equations by inspection (e.g. For x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

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