American Highschool Academy Unit 3 Perfect Square Trinomial Questions

This assignment is multiple choice questions, and a separate assignment. SHOW WORK this is a graded assignment. the multiple choice questions, you do not have to show work but for the project assignment you must show work. please take your time doing this.

Solve the equation by completing the square.
2×2 – 7x = -12
A
B
C
D
Solve the equation by completing the square.
x2 – 10x + 28 = 0
x ≈ 3.3, x ≈ 6.7
x = 5 + i√3, x = 5 − i√3
x ≈ 18.5, x ≈ 1.5
x = 10 + i√3 , x = 10 − i√3
Rewrite the equation so that the left side is a factored perfect square.
3×2 – 4x = 2
A
B
C
D
Write an equation equivalent to the one below by writing the trinomial as a perfect square trinomial.
x2 + 8x + 9 = – 9
x2 + 8x + 16 = 16
x2 + 8x + 16 =- 2
x2 + 8x + 64 = 46
x2 + 8x + 64 = 64
Find the value of c that will make the expression a perfect square trinomial.
x2 + 0.6x + c
0.3
0.36
0.9
0.09
Write an equation equivalent to the one below by writing the trinomial as a perfect square trinomial.
Write an equation equivalent to the one below by writing the trinomial as a perfect square trinomial.
x2 – 4x + 1 = 0
x2 – 4x + 4 = -3
x2 – 4x + 5 = 0
x2 – 4x + 4 = 3
x2 – 4x + 4 = 5
Find the value of c that will make the expression a perfect square trinomial.
x2 – 15x + c
-7.5
7.5
-56.25
56.25
Rewrite the equation by factoring the perfect square trinomial.
x2 + 8x + 16 = 7
(x + 4)2 = 7
(x – 4)2 = 7
(x + 8)2 = 7
(x – 8)2 = 7
Rewrite the equation by factoring the perfect square trinomial.
x2 + 12x + 36 = 25
(x – 6)2 = 5
(x – 6)2 = 25
(x + 6)2 = 25
(x + 6)2 = 5
Solve the quadratic equation by using the quadratic formula.
3×2 + 4x + 10 = 0
A
B
C
D
Solve the quadratic equation by using the quadratic formula.
0.4×2 + x – 0.3 = 0
A
B
C
D
Solve the quadratic equation by using the quadratic formula.
-3×2 – 5x + 2 = 0
In which case would it be best to use the “Factoring Method” to solve the trinomial equation?
x2 + 4x = -5
4.3×2 + 2.4x – 3 = 0
x2 – 4x + 3 = 0
Which graph shows a quadratic function which has a discriminant of 0?
A.
C.
B.
D.
A
B
C
D
If a quadratic equation has a discriminant of 16, what is not always true about its solutions?
All solutions are rational numbers
All solutions are real numbers
All solutions are integers
There are two solutions
How many real solutions does a quadratic equation have if it discriminant is 103
0
1
2
3
How many real solutions does a quadratic equation have if its discriminant is- 3?
0
1
2
3
Find the discriminant of the quadratic equation.
-12×2 + 5x + 2 = 0
121
71
-71
-121
Find the discriminant of the quadratic equation.
9×2 – 6x – 4 = 0
108
180
-108
-180
Which graph shows the function below?
y = (⅓)(x – 1)2 + 2
A.
C.
B.
D.
A
B
C
D
Which of the following functions is shown in the graph below?
y = (x – 1)2 + 2
y = -2(x – 1)2 + 2
y = 2(x + 1)2 + 2
y = (x + 1)2 + 2
Which of the following shows the following equation in vertex form?
y = -4×2 + 16x + 11
-y = 4(x – 4)2 – 53
y = -4(x + 4)2 – 53
y = -4(x – 2)2 + 27
y = -4(x + 4)2 + 75
Which of the following shows the following equation in vertex form?
y = x2 – 8x + 18
y = (x – 4)2 + 2
y = (x – 8)2 – 46
y = (x – 4)2 + 34
y = (x – 8)2 + 2
Describe the translation from the graph of y = x2 if you are given the function below:
y = (x – 3)2+ 2
The graph is translated three units to the left and two units up.
The graph is translated three units to the left and two units down.
The graph is translated three units to the right and two units down.
The graph is translated three units to the right and two units up.
Which of the following functions is shown in the graph below?
y = (x – 6)2 – 9
y = (x + 9)2 – 6
y = (x + 6)2 + 9
y = (x – 9)2 – 6
Which correctly identifies the values of the parameters a, h, and k for the function below?
f(x) = 2(x – 3)2 + 4
a = 2, h = -3, k = 4
a = 2, h = 3, k = 4
a = -2, h = 3, k = -4
a = 2, h = 3, k = -4
Which graphs shows the graph of the function below?
y = (x – 2)2 + 4
A.
C.
A
B
C
D
B.
D.
Describe the translation from the graph of y = x2 if you are given the function below:
y = (x + 2)2 – 4
The graph is translated to the right 2 units and down 4 units.
The graph is translated to the left 2 units and down 4 units.
The graph is translated to the left 2 units and up 4 units.
The graph is translated to the right 2 units and up 4 units.
Which of the following equations shows a parabola in vertex form.
y = 2×2 + 3x – 4
y – 4 = 2(x2 + 2)
y = -(x – 5)2 – 3
y = 2(x2 + 1)- 2
Which graph shows the inequality?
y ≥ 2×2 + x – 3
A.
B.
C.
D.
A
B
C
D
The graph of a quadratic inequality is shown below. Use the graph to find the solutions to the inequality in terms of x.
x ≤ -2 or x ≥ 1
x < 2 or x > 1
-2 ≤ x ≤ 1
-2 < x < 1 The graph of a quadratic inequality is shown below. Use the graph to find the solutions to the inequality in terms of x. x < -1 or x > 4
x ≤ -1 or x ≥ 4
-1 ≤ x ≤ 4
-1 < x < 4 Choose the statement that is true about the graph of the quadratic inequality. y ≤ 5x2 + 6x + 2 Points on the parabola are not solutions. The vertex is (-3/5, 1/5) . The parabola opens down. (0, 0) is not a solution. Which ordered pair is not a solution to the inequality? y ≥ 2x2 - 7x - 10 (0, -4) (-1,-1) (4,-13) (5,15) Which quadratic inequality is graphed below? y ≥ x2 + 2 y ≤ x2 - 2 y ≥ (x - 2)2 y ≥ (x + 2)2 Find the solutions to the inequality. x2 + 7x - 8 > 0
x < - 8 or x > 1
-8 4
x < -4 or x > 7
-7 < x < 4 -4 < x < 7 Which graph shows the inequality? y < 2x2 + 3x - 5 A. C. A B C D B. D. If (x + 1)(x - 2) is positive, which statement must be true? x < - 1 or x > 2
x > – 1 or x < 2 -1