Algebra: 8.2.3 Graphing with Technology
Solutions
Name ______________________________
Block _____ Date ______
Bell Work 1/16 Factor each quadratic equation completely, and then find the roots. Show sufficient work.
a.
y = x2 + 4x + 3
1
𝑦 = (𝑥 + 3)(𝑥 + 1)
𝑥
3
𝑥 𝑥2
3𝑥
𝑥
3
b.
y = 4x2 − 1
𝑦 = (2𝑥 + 1)(2𝑥 − 1)
Use Graphing Calculator Technology:
8-77. Find the zeros, and vertex, y-intercept and graph y = x2 − 3x − 7.
a. What keystrokes are used to graph?
Y = 〈𝐢𝐧𝐩𝐮𝐭 𝐞𝐪𝐮𝐚𝐭𝐢𝐨𝐧〉, Window 〈𝐚𝐝𝐣𝐮𝐬𝐭〉, Graph
b. What keystrokes are used to find the zeros?
2nd, Trace, 2, Left 〈𝐞𝐧𝐭𝐞𝐫〉, Right 〈𝐞𝐧𝐭𝐞𝐫〉 〈𝐞𝐧𝐭𝐞𝐫〉
Zeros: ≈ −𝟏. 𝟓 and 𝟒. 𝟓
-1.5
4.5
c. What keystrokes are used to find the y-intercept?
Y-Intercept = −𝟕
Trace, 0 〈𝐞𝐧𝐭𝐞𝐫〉
-7
d. What keystrokes are used to find the vertex?
(1.5, -9.25)
2nd, Trace, 3 or 4, Left 〈𝐞𝐧𝐭𝐞𝐫〉, Right 〈𝐞𝐧𝐭𝐞𝐫〉 〈𝐞𝐧𝐭𝐞𝐫〉
Vertex ≈ (𝟏. 𝟓. −𝟗. 𝟐𝟓)
8-78. Find the zeros, and vertex, y-intercept and graph y = −x2 + 3x + 6
(1.5, 8.25)
Zeros
≈ −𝟏. 𝟒 and 𝟒. 𝟒
6
Vertex ≈ (𝟏. 𝟓. 𝟗. 𝟐𝟓)
y-intercept = 𝟔
-1.4
4.4
8-79. Graph y = 3(x − 2)2 −5
a. How does this graph compare to the parent 𝑦 = 𝑥 2 ?
7
3 times as steep, right 2, down 5
b. Find the roots: ≈ 𝟎. 𝟕 and 𝟑. 𝟑
.7
3.3
c. Find the y-intercept. 𝟕
(2, -5)
d. Find the vertex. (𝟐, −𝟓)
𝑦 = 3(𝑥 − 2)2 − 5
𝑦 = 3(𝑥 2 − 4𝑥 + 4) − 5
e. Simplify this equation.
𝑦 = 3𝑥 2 − 12𝑥 + 12 − 5
𝒚 = 𝟑𝒙𝟐 − 𝟏𝟐𝒙 + 𝟕
−2 −2𝑥
4
𝑥 𝑥2
−2𝑥
𝑥
−2
8-80. Graph y = (x + 1)2 − 16
a. How does this graph compare to the parent 𝑦 = 𝑥 2 ?
Left 1, down 16
b. Find the roots: −𝟓 and 𝟑
3
-5
c. Find the y-intercept. −𝟏𝟓
d. Find the vertex. (−𝟏, −𝟏𝟔)
-15
(-1, -16)
2
e. Simplify this equation. 𝑦 = (𝑥 + 1) − 16
𝑦 = 𝑥 2 + 2𝑥 + 1 − 16
𝒚 = 𝒙𝟐 + 𝟐𝒙 − 𝟏𝟓
+1 1𝑥
1
𝑥 𝑥2
1𝑥
𝑥
+1
2
8-81. Graph y = (x + 2) − 3
a. How does this graph compare to the parent 𝑦 = 𝑥 2 ?
Left 2, down 3
b. Find the roots: −𝟑. 𝟕 and −𝟎. 𝟑
1
c. Find the y-intercept. 𝟏
d. Find the vertex. (−𝟐, −𝟑)
e. Simplify this equation.
-3.7
+2 2𝑥
4
𝑥 𝑥2
2𝑥
𝑥
+2
𝑦 = (𝑥 + 2)2 − 3
𝑦 = 𝑥 2 + 4𝑥 + 4 − 3
𝒚 = 𝒙𝟐 + 𝟒𝒙 + 𝟏
-.3
(-2, -3)
8-83. Use the Zero Product Property to find the roots of the quadratics below.
−1 −3𝑥
a. 3x2 − 7x + 4 = 0
𝒙=𝟎
𝑥+6= 0
𝒙 = −𝟔
4
𝑥−1= 0
𝒙=𝟏
𝑥 3𝑥 2 −4𝑥
3𝑥
b. x2 + 6x = 0
𝑥 (𝑥 + 6) = 0
c. (x + 5)(−2x + 3) = 0
𝑥+5= 0
𝒙 = −𝟓
3𝑥 − 4 = 0
3𝑥 = 4
𝟒
𝒙=
𝟑
−4
−2𝑥 + 3 = 0
−2𝑥 = −3
𝟑
𝒙=
𝟐
The following are ANSWERS ONLY. Show SUFFICIENT WORK for credit!
8-85. Solve the equations below for x. Check your solutions. (factor, set factors = 0, solve each)
𝒙=−
𝟐
𝟑
a. (6x −18)(3x + 2) = 0
𝒙=𝟑
b. x2 − 7x + 10 = 0
𝒙=𝟓
𝒙=𝟐
c. 2x2 + 2x −12 = 0
𝒙 = −𝟑
𝒙=𝟐
d. 4x2 − 1 = 0
𝒙=−
𝟏
𝟐
𝒙=
𝟏
𝟐
8-86. Sketch each parabola below with the given information.
a. A parabola with x-intercepts (2, 0) and (7, 0) and y-intercept (0, −8).
b. A parabola with exactly one x-intercept at (−1, 0) and y-intercept (0, 3).
c. The parabola represented by the equation y = (x + 5)(x − 1).
a.
b.
c.