Transcript Unit 5 Review - Campbell County High School

Unit 5 Review:
Quadratics and
Beyond
Honors Analysis
Test Topics
 Find
x intercepts of quadratics (set y = 0)
 Find y intercepts of quadratics (set x = 0)
 Determine the vertex of a parabola using
the vertex formula (x = -b/2a)
 Apply quadratic analysis to real-life
scenarios
Test Topics
 Factoring
Techniques:
 1) Factor out the GCF
 2) Difference of Squares
 3) Trinomials (x2 + bx + c)
 4) Trinomials (ax2 + bx + c – guess &
check)
 4) Grouping
 Complete the square
 Write parabola in vertex form by
completing the square
 Graph a parabola using vertex form
 Optimization Problems (Videos online)
Find all real solutions by
factoring:
2
6𝑥 − 7𝑥 = 5
Solution:
2
6𝑥 − 7𝑥 − 5 = 0
(3x – 5)(2x + 1) = 0
x = 5/3 or x = -1/2
Find all real solutions by
factoring:
3
5𝑥 = 5𝑥
Solution
3
5𝑥 − 5𝑥 = 0
2
5x(𝑥 − 1) = 0
5x(x+1)(x – 1) = 0
x = 0 or -1 or 1
Find all real solutions by
factoring:
3
2
4𝑥 − 8𝑥 − 12𝑥 = 0
Solution:
3
2
4𝑥 − 8𝑥 − 12𝑥 = 0
2
4x(𝑥 − 2𝑥 − 3) = 0
4x(x – 3)(x + 1) = 0
x = 0 or x = 3 or x = -1
Find all real solutions by
factoring:
3
9𝑥 = 25𝑥
Solution:
3
9𝑥 − 25𝑥 = 0
2
x(9𝑥 − 25) = 0
x(3x + 5)(3x – 5) = 0
x = 0; x = -5/3; x = 5/3
Find all real solutions by
factoring:
4
3
2
8𝑥 − 8𝑥 − 6𝑥 = 0
Solution:
4
3
2
8𝑥 − 8𝑥 − 6𝑥 = 0
2
2
2𝑥 4𝑥 − 4𝑥 − 3 = 0
2
2𝑥 2𝑥 + 1 2𝑥 − 3 = 0
x = 0 or x = -1/2 or 3/2
Find all real solutions by
factoring:
3
2
𝑥 − 𝑥 − 4𝑥 + 4 = 0
Solution:
3
𝑥 −
2
𝑥 − 4𝑥 + 4 = 0
2
𝑥 𝑥−1 −4 𝑥−1 =0
2
𝑥−1 𝑥 −4 =0
𝑥−1 𝑥−2 𝑥+2 =0
x = 1 or 2 or -2
Find all real solutions by
factoring:
4
3
2
2𝑥 + 3𝑥 − 18𝑥 − 27𝑥 = 0
Solution:
4
2𝑥
+
3
3
3𝑥
−
2
18𝑥
− 27𝑥 = 0
2
𝑥(2𝑥 + 3𝑥 − 18𝑥 − 27) = 0
2
x[𝑥 2𝑥 + 3 − 9 2𝑥 + 3 ] = 0
2
𝑥 2𝑥 + 3 𝑥 − 9 = 0
x(2x + 3)(x + 3)(x – 3) = 0
x = 0 or -3/2 or -3 or 3
Find all real solutions by
factoring:
5
3
−2𝑥 + 26𝑥 − 72𝑥 = 0
Solutions
−2𝑥 5 + 26𝑥 3 − 72𝑥 = 0
−2𝑥 𝑥 4 − 13𝑥 2 + 36 = 0
−2𝑥 𝑥 2 − 9 𝑥 2 − 4 = 0
−2𝑥 𝑥 + 3 𝑥 − 3 𝑥 + 2 𝑥 − 2 = 0
x = 0; x = -3; x = 3; x = -2; x = 2