1.
The equation of the parabola A is
$y$ = 
$x$^{2}. Find the equation of the parabola B that is obtained by the transformation of A.
Solution:
The equation of the parabola A is = y =  x^{2}.
The parabola A has been transformed 4 units up to get the parabola B.
That is, y =  (x ^{2}) + 4.
So, the equation of the red parabola is y =  x ^{2} + 4.
Correct answer : (3)
2.
Identify the equation that transforms the parabola
$A$,
$y$ = 5$x$^{2} + 2 to the parabola
$B$.
Solution:
The equation of the parabola A is y = 5x^{2} + 2.
The parabola A has been transformed 6 units down to get the parabola B.
that is, y = (5x^{2} + 2)  6 = 5x^{2}  4.
So, the equation of the parabola B is y = 5x^{2}  4.
Correct answer : (1)
3.
The graph of
$y$ = 3$x$^{2}  9$x$ is shown. Estimate the solution of
3$x$^{2}  9$x$ = 0 using the graph.
Solution:
The xintercepts in the graph of the equation y = ax^{2} + bx + c are the solutions of the related equation ax^{2} + bx + c = 0.
The graph intersects the xaxis at (0, 0) and (3, 0).
So, 0 and 3 are the solutions of the equation.
Correct answer : (2)
4.
Estimate the solution of
$x$^{2}  $x$ = 6 using the graph.
Solution:
From the figure, the graph intersects the xaxis at two points ( 2,0) and (3,0).
The xintercepts of the curve are  2 and 3.
[xcoordinate of the point where curve meets xaxis.]
x^{2}  x = 6
[Original equation.]
(2)^{2}  ( 2) = 6
[Substitute the x intercept =  2.]
6 = 6
[Simplify.]
(3)^{2}  (3) = 6
[Substitute the x intercept = 3.]
6 = 6
[Simplify.]
Both the values satisfy the equation. So, 2 and 3 are the solutions of the equation.
Correct answer : (1)
5.
Estimate the solution of
2$x$^{2}  $x$ = 3 using the graph.
Solution:
From the figure, the graph intersects the x  axis at two points (1, 0) and ( 3 / 2, 0).
The xintercepts of the curve are 1 and 3 / 2.
2x^{2}  x = 3
[Original equation]
2(1)^{2}  (1) = 3
[Substitute xintercept as 1.]
3 = 3
[Simplify.]
2( 32)^{2}  (32) = 3
[Substitute xintercept as 3 / 2.]
3 = 3
[Simplify.]
Both the values satisfy the equation. So, 1 and 3 / 2 are the solutions of the equation.
Correct answer : (1)
6.
Find the solution of  3$x$^{2} =  27 using a graph.
Solution:
 3
x^{2} =  27
[Original equation]
x^{2} = 9
[Divide  3 on each side]
x^{2}  9 = 9  9
[Subtract 9 from each side]
x^{2}  9 = 0
[Simplify.]
Sketch the graph of the related quadratic function
y =
x^{2}  9 as shown below.
From the graph, the
xintercepts appear to be  3 and 3.
[Estimate the values of the
xintercepts.]
So,  3 and 3 are the solutions of the equation.
Correct answer : (2)
7.
Using a graph, estimate the solution of  $x$^{2} + 9$x$  20 = 0.
Solution:

x^{2} + 9
x  20 = 0 can be written in standard form as
y = 
x^{2} + 9
x  20.
Sketch the graph of the quadratic function
y = 
x^{2} + 9
x  20 as:
From the graph, the
xintercepts are 4 and 5.
[Estimate the values of the
xintercepts.]
 (4)
^{2} + 9(4)  20 = 0
[Substitute the
xintetcept = 4 in the equation 
x^{2}  20 = 0.]
0 = 0
[Simplify.]
 (5)
^{2} + 9(5)  20 = 0
[Substitute the
xintetcept = 5 in the equation 
x^{2}  20 = 0.]
0 = 0
[Simplify.]
Both the values satisfy the equation. So, 4 and 5 are the solutions of the equation.
Correct answer : (3)
8.
Find the roots of the quadratic equation
$x$^{2} + 5 = 6 using the graph.
Solution:
The equation in the standard form is ax^{2} + bx + c = 0.
x^{2} + 5 = 6
[Original equation.]
x^{2} + 5  6 = 6  6
[Subtract 6 from each side.]
x^{2}  1 = 0
[Simplify.]
The graph appears to intersect the xaxis at the points (1, 0) and (1, 0).
From the graph, the xintercepts appear to be 1 and 1.
[Estimate the values of the xintercepts.]
By substituting x = 1 and x = 1 in x^{2}  1 = 0, 1 and 1 are obtained.
So, 1 and 1 are the roots of the quadratic equation.
Correct answer : (1)
9.
Using the graph, find the solution of
2$x$^{2} + 8 = 0.
Solution:
2x^{2} + 8 = 0 is written in the standard form as y = 2x^{2} + 8.
The graph intersect the xaxis at points (2, 0) and (2, 0).
From the graph, the xintercepts are 2 and 2.
[Estimate the values of the xintercepts.]
2(2)^{2} + 8 = 0
[Substitute x = 2 in the equation 2x^{2} + 8 = 0.]
0 = 0
[Simplify.]
2(2)^{2} + 8 = 0
[Substitute x = 2 in the equation 2x^{2} + 8 = 0.]
0 = 0
[Simplify.]
Both the values satisfy the equation. So, 2 and 2 are the solutions of the equation.
Correct answer : (3)
10.
Using a graph, identify the roots of the quadratic equation  $x$^{2}  2$x$ + 3 = 0.
Solution:

x^{2}  2
x + 3 = 0 is written in standard form as
y = 
x^{2}  2
x + 3.
Sketch the graph of the quadratic function
y = 
x^{2}  2
x + 3 as:
From the graph, the
xintercepts are  3 and 1.
[Estimate the values of the
xintercepts.]
 ( 3)
^{2}  2( 3) + 3 = 0
[Substitute
x =  3 in the equation 
x^{2}  2
x + 3.]
0 = 0
[Simplify.]
 (1)
^{2}  2(1) + 3 = 0
[Substitute
x = 1 in the equation 
x^{2}  2
x + 3.]
0 = 0
[Simplify.]
Both the values satisfy the equation. So,  3 and 1 are the roots of the equation.
Correct answer : (3)