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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
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10.3 Solving Quadratic Equations
I can solve quadratic equations by graphing.
I can solve quadratic equations by using square roots.
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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
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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
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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
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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
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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.
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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.