Write Quadratic Equations from Graphs
Authored by Tracey Long
Mathematics
9th - 12th Grade
CCSS covered
Used 269+ times
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10 questions
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1.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
Write a quadratic equation given the x intercepts and one other point.
Step 1: Write the factors.
The intercepts of this function are (6, 0) and (8, 0). Write the factors.
(x-6) and (x-8)
(x+6) and (x+8)
(x-6) and (x+8)
(x+6) and (x-8)
Tags
CCSS.HSF-IF.C.7A
2.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
Write a quadratic equation given the x intercepts and one other point.
Step 2: Find a.
Now that you know that the factors are (x-6) and (x-8), you must find a. Plug the coordinates of the vertex (7, 1) in for x and y and solve for a.
y = a(x-6)(x-8)
What is the value of a?
a = 1
a = -1
a = 7
a = -7
3.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
Write a quadratic equation given the x intercepts and one other point.
Step 3: Write the equation in factored form.
Now, you know that the factors are (x-6) and (x-8) and a = -1. Write the equation of the graph in factored form.
-(x-6)(x-8)
-(x+6)(x+8)
(x-6)(x+8)
(x+6)(x-8)
Tags
CCSS.HSA-SSE.B.3B
CCSS.HSF-IF.C.8A
4.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
Now, take the factored form and write it in Standard Form (ax2+bx+c=0) by double distributing (or FOIL).
-(x-6)(x-8)=0
x2+2x-15=0
-x2+14x -48=0
- x2+8x-15=0
x2 + 5x -16=0
5.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
Write a quadratic equation given the x intercepts and one other point.
Put the steps together.
- Find the factors.
- Solve for a by substituting in the extra point.
- Write the equation in factored form.
The roots of the function are (-3, 0) and (5, 0).
The point (4, -3) is also on the graph.
y=4(x+3)(x-5)
y=3/7(x-3)(x+5)
y=-3(x-3)(x+5)
y=3/7(x+3)(x-5)
6.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
Write a quadratic equation in vertex form given the vertex and another point.
- Substitute the coordinates of the vertex (1, -4) in for h and k.
Vertex form: y=a(x-h)2+k
(x+1)2-4=y
(x-1)2-4=y
(x + 1)(x - 3)=y
x2 +2x - 3=y
7.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
Convert this equation in vertex form to standard form.
(x-1)2 -1
x2 -2x - 2
x2+x-2
x2+2
x2-2x
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