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Worksheets

Writing Quadratics Given Points/Solutions

Total questions: 23

Worksheet time: 1hrs 10mins

Name
Class
Date
1.

Which quadratic function in vertex form can be represented by the graph that has a vertex at (3,-7) and passes through the point (1,-10)?

a)
b)
c)
d)
2.

Which function is best represented by this graph?

a)
b)
c)
d)
3.
Write the equation of the quadratic function that has a vertex of (-5, 9) and passes through the point (-7, -15).
a)
y = 6(x + 5)2 + 9
b)
y = -6(x - 5)2 + 9
c)
y = 6(x - 5)2 + 9
d)
y = -6(x + 5)2 + 9
4.

Write the equation of the quadratic function that has a x-intercepts at (2, 0) and (4, 0) and passes through the point (3, 4).

a)

y = -4(x - 2)(x - 4)

b)

y = -4(x + 2)(x + 4)

c)

y = 4(x - 2)(x - 4)

d)

y = -0.25(x - 2)(x - 4)

5.

What are the solutions? Hint: look at x-intercepts

a)

x= -5

b)

x= -1 and x = 5

c)

(2,-9)

d)

Cannot be determined

6.

When looking at a quadratic graph, the solution(s) are always the _____________.

a)

y-intercept

b)

vertex

c)

x-intercept(s)

d)

axis of symmetry

7.
What is the green dashed line called?
a)
roots or x-intercepts
b)
parabola
c)
axis of symmetry
d)
line of dashes
8.
Which quadratic function in vertex form best represents the graph that has a vertex at (4,-1) and passes through the point (8, 3)?
a)
f(x) = 1/4(x - 4)2 - 1
b)
f(x) = 4(x - 4)2 - 1
c)
f(x) = 4(x + 4)2 - 1
d)
f(x) = 1/4(x + 4)2 - 1
9.
What is another name for the x-intercepts of a quadratic?
a)
y-intercepts
b)
zeros
c)
x-axis
d)
none of these
10.
Is this a max or min?
a)
max
b)
min
c)
cannot be determined
11.
What is the green dot on the parabola called?
a)
maximum
b)
minumum
c)
roots
d)
zeros
12.
What are the green dots called?
a)
axis of symmetry
b)
vertex
c)
parabola
d)
roots or x-intercepts
13.

What is the equation in vertex form?

a)

y = -4(x + 3)2 - 4

b)

y = 4(x - 3) - 4

c)

y = 4(x + 3)2 + 4

d)

y = -4(x - 3)2 + 4

14.
Write the equation of the quadratic function that has a x-intercepts at 2 and 4 and passes through the point (3, 4).
a)
y = -4(x - 2)(x - 4)
b)
y = -4(x + 2)(x + 4)
c)
y = 4(x - 2)(x - 4)
d)
y = -0.25(x - 2)(x - 4)
15.

If given the equation y = 3(x + 5)2 - 4, what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

16.
The axis of symmetry line passes through which point?
a)
y-intercept
b)
any random point
c)
vertex
d)
symmetrical point for the vertex
17.
Write the equation of the quadratic function that has a vertex of (4,-1) and passes through the point (8, 3).
a)
y = 1/4(x - 4)2 - 1
b)
y = 4(x - 4)2 - 1
c)
y = 4(x + 4)2 - 1
d)
y = 1/4(x + 4)2 - 1
18.

What is the domain of this quadratic graph?

a)

y ≥ 3

b)

y ≤ 3

c)

d)

y ≤ 2

19.
Does this graph have a maximum or minimum?
a)
Minimum
b)
Maximum
20.
Does this parabola have a maximum or minimum?
REMEMBER MAXIMUM IS THE HIGHEST AND MINIMUM IS THE LOWEST. 
a)
Maximum
b)
Minimum
21.
If the a value is positive, which direction does the graph open?
a)
up
b)
down
c)
left
d)
right
22.
If the a value is negative, which direction does the parabola open?
a)
up
b)
down
c)
left
d)
right
23.
Which of the following equations matches standard form of a quadratic?
a)
y = mx + b
b)
y = ax2 + bx + c