Day 5

Simplify each expression:

1. 36 2. 81 3. 121

3. 1.44 4. 0.25 5. 1.21

1 1 496. 7. 8.

4 9 100

6 9 11

1.2 0.5 1.1

1 1 7

2 3 10

10.3 Solving Quadratic Equations

I can solve quadratic equations by graphing.

I can solve quadratic equations by using square roots.

A quadratic equation is an equation that can be written in the form , where a 0.

This form is called the standard form of a quadratic equation.

2 0ax bx c

A quadratic can have 2, 1, or no real solutions.

Solutions of a quadratic equation are called roots of the equation or zeros of the function or x-intercepts.

10.3 Solving Quadratic Equations

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

x

y

Solving Quadratics by Graphing

Graph the following and determine their solutions.

Remember: Solutions are where the graph crosses the x-axis. There can be 2, 1, or none.

2 4 0x Ex. 1

x y

– 2– 1 0 1 2

0– 3– 4– 3 0

2 2x and

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

x

y

Solving Quadratics by Graphing

2 0x Ex. 2

x y

– 2– 1 0 1 2

4 1 0 1 4

0x

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

x

y

Solving Quadratics by Graphing

2 4 0x Ex. 3

x y

– 2– 1 0 1 2

8 5 4 5 8

Noreal solutions

Solving Quadratics by Using Square Roots

22 98 0x Ex. 4

Solve the following for x.

22 98x 2 49x

Add 98 to both sides.

Divide both sides by 2.

7x Square root both sides.

Remember: When you square root something, it gives you a plus and a minus answer.

Solving Quadratics by Using Square Roots

2 25 0t Ex. 5

Solve each equation.

2 25t 5x

23 12 12n Ex. 6

23 0n

0n

2 0n

22 32 0g Ex. 7

22 32g

NoSolution

2 16g Can’t take the square

root of a negative.