Unit 10: Quadratic Functions

Topic: Solving Quadratics by Factoring & Square Roots

DefinitionsZeros of a quadratic functionSolutions of a quadratic functionRoots of a quadratic function

All three refer to the same thing!The value(s) of x that make y = 0 (x-intercepts of the

parabola).

How can you solve a quadratic equation without graphing it?Set the equation equal to zero & factor it.Use the Zero Product Property to determine the

solutions from your factors.Zero Product Property: If ab = 0, then either a = 0 or

b = 0.

Solving Quadratics by FactoringFind factors of ac whose sum is b.

2 & 9

1863

0)23)(3(

0)23)(3(3

0)23)(93(

xx

xx

xx

0)23)(3(

0)3(2)3(3

0)62()93(

062932

2

xx

xxx

xxx

xxx

Factor using your preferred method.

Ms. Bonilla Method Group & Factor Method

3 𝑥2+7𝑥−6=0

If you use the Punnett Square, the 4 terms from Group & Factor go in the square.

Solving Quadratics by FactoringUse Zero Product Property to find solutions for x. For the statement to be true, either x + 3 =0 or 3x – 2 = 0. Solve each of those for x.

03 x 023 x3x

32

23

x

x

32or 3x

( 𝑥+3 )(3 𝑥−2)=0

Solving Quadratics by FactoringSet the equation equal to 0 (move 4x to the other side.)

042 xx

0)4( xx

Since there is no c, this can’t be factored as a regular quadratic. All we can do is factor out a GCF.

𝑥2=4 𝑥

Use Zero Product Property to solve for x.

0x 04 x4x

4or 0x

Square roots can be used to solve quadratic equations when b = 0.

REMEMBER: Square roots actually have two solutions, one + & one -.Example: 5or 525

Solving Quadratics by Square Roots

4252 x

25

4252

4252

x

x

x

254 2 x Divide both sides by a (leave the result as a fraction!).

Take the square root of both sides (Remember that a square root distributes to a fraction just like an exponent).

This is why we leave the fraction; both numerator & denominator are perfect squares.

Solving Quadratics by Square Roots

Journal EntryTITLE: Solving Quadratics CYK

Things I Already Knew: Identify at least 2New Things I Learned: Identify at least 2Questions I Still Have: Identify at least 2

HomeworkQuest: Solving Quadratics by Factoring &

Square RootsDue 5/18