!...

Algebra 2 & Trigonometry -‐ Quadratics Review

𝑎𝑥! + 𝑏𝑥 + 𝑐 = 0 Factoring– Put equation in standard form. Factor Set all factors equal to zero. 1. Solve for x:

2. Solve for x; = 0 3. Solve for x: = 0 4. Solve for t: = 0 Completing the Square – 1. Add constant to both sides 2. Make coefficient of 𝑥! equal 1

-‐ divide both sides by a 3. Divide the coefficient of x by 2, square it and add to both sides 4. Factor the perfect square trinomial – take the square root of both sides (don’t forget the ± !) and solve for x. example 3𝑑! + 5𝑑 − 12 = 0 1. Subtract 12 3𝑑! + 5𝑑 = −12 2. divide by 3: 𝑑! + !

!𝑑 = −4

3. Add !"!" (half of !

! , squared) to both sides

𝑑! + !!𝑑 + !"

!"= −4+ !"

!"

4. Factor , take the square root, and solve

𝑥 + !!

!= !!!"

!"

𝑥 + !!

! = ± !!"

!"

𝑥 + !

!= ± !!"

!

𝑥 = !!+ ± !!"

! = ! ± !!"

!

Solve by completing the square: 5. 4𝑥! + 8𝑥 − 2 = 0 6. 𝑥! − 6𝑥 − 4 = 0 Quadratic Formula –

𝑥 = −𝑏 ± 𝑏! − 4𝑎𝑐

2𝑎

7. Solve for x in simplest form:

8. In physics class, Tara discovers that the behavior of electrical power, x, in a particular circuit can be represented by the function . If

, solve the equation and express your answer in simplest form. 9. Find the roots of the equation 10. A rectangular patio measuring 6 meters by 8 meters is to be increased in size to an area measuring 150 square meters. If both the width and the length are to be increased by the same amount, what is the number of meters, to the nearest tenth, that the dimensions will be increased? 11. As shown in the accompanying diagram, the hypotenuse of the right triangle is 6 meters long. One leg is 1 meter longer than the other. Find the lengths of both legs of the triangle, to the nearest hundredth of a meter.


𝑎𝑥! + 𝑏𝑥 + 𝑐 = 0 Discriminant – 𝑏! − 4𝑎𝑐

(it’s the stuff under the radical)

• if it’s negative – roots are imaginary • if it’s zero –

roots are real, rational, & equal • if it’s positive and

a perfect square roots are real, rational & unequal not a perfect square roots are real, irrational & unequal 12. Which value of c would make the roots of the equation real, rational, and equal? 1) 9 3) 18

2) -‐9 4) -‐18 13. Use the discriminant to determine all values of k that would result in the equation

having equal roots. 14. What is one value of k for which

has real roots? Quadratic Inequalities Solve as an equation, then – Less than? Graph between two points: Greater than? Graph outside the two points: 15. What is the solution set of the inequality

? 1) 2) 3) 4)

(test taking tip: it’s a “less than” – so x is between)

16. What is the solution set of the inequality ?

1) 2) 3) 4)

(test taking tip: it’s a “greater than” – so x is outside) 17. Which graph represents the solution set of the inequality ?

1)

2)

3)

4)

18. What is the solution set for the inequality

?

19. what is the solution set of ?

A B 𝐴 ≤ 𝑥 ≤ 𝐵

A B 𝑥 ≤ 𝐴 or 𝑥 ≥ 𝐵


𝑎𝑥! + 𝑏𝑥 + 𝑐 = 0

!...

Documents

Transcript of !...