Math - Deriving Quadratic Equations and Functions

Question

A. Determine the quadratic equation and function whose graph passes through the given coordinates in the table of values.

1.   

X	-3	-2	-1	0	1	2	3
y	-5	-8	-9	-8	-5	0	7

2.   

X	-3	-2	-1	0	1	2	3
y	-5	-8	-9	-8	-5	0	7
X	-1	0	1	2	3	4	5
y	-10	-2	0	-4	-14	-30	-52

3.   

X	-4	-3	-2	-1	0	1	2
y	16	9	4	1	0	1	4

4.   

X	-3	-2	-1	0	1	2	3
y	-10	-5	-2	-1	-2	-5	-10

B. Determine the quadratic equation and function whose zeros are:

1. 2 and -7

2. 5 and -5

3. 3i

4. -2 and 1/3

5. 1 and 4

Answer 1

1) vertex is (-1,-9)

y = a(x+1)^2 -9

plug in any other point to solve for a, such as (1, -5)

-5 = a(1+1)^2 - 9

4a = 4

a = 1

the quadratic equation is y=(x+1)^2 - 9

2) y = (x+1)^ -9

for 2nd data, zero or x intercept is 1, the point (1,0) y intercept =-2, the point (0, -2) it's a downward opening parabola

y =-x^2 + x - 2

3) y=x^2

4) y =-x^2 -1

B1) zeros 2 and -7

y = (x-2)(x+7)

B2) 5 and -5

y = (x-5)(x+5)

B3) 3i, -3i (they come in conjugate pairs)

y =x^2 +9

B4) -2 and 1/3

y = (x+2)(x-1/3)

B5) 1 and 4

y =(x-1)(x-4)