Question

the table below represents a quadratic relationship.

x	1	2	3	4
y	10	32	64	106

which equation best models the data? (round to one decimal place if needed)
a ( y = 7x^2 - 2x + 5 )
b ( y = -2.3x^2 + 1.4 )
c ( y = 5x^2 + 7x - 2 )
d ( y = x^2 + 1x + 10 )

Explanation:

Step1: Test x=1 for Option A

Substitute $x=1$ into $y=7x^2-2x+5$:
$y=7(1)^2-2(1)+5=7-2+5=10$

Step2: Test x=2 for Option A

Substitute $x=2$ into $y=7x^2-2x+5$:
$y=7(2)^2-2(2)+5=28-4+5=29$ (does not match 32)

Step3: Test x=1 for Option B

Substitute $x=1$ into $y=-2.3x^2+1.4$:
$y=-2.3(1)^2+1.4=-0.9$ (does not match 10)

Step4: Test x=1 for Option C

Substitute $x=1$ into $y=5x^2+7x-2$:
$y=5(1)^2+7(1)-2=5+7-2=10$

Step5: Test x=2 for Option C

Substitute $x=2$ into $y=5x^2+7x-2$:
$y=5(2)^2+7(2)-2=20+14-2=32$

Step6: Test x=3 for Option C

Substitute $x=3$ into $y=5x^2+7x-2$:
$y=5(3)^2+7(3)-2=45+21-2=64$

Step7: Test x=4 for Option C

Substitute $x=4$ into $y=5x^2+7x-2$:
$y=5(4)^2+7(4)-2=80+28-2=106$

Step8: Test x=1 for Option D

Substitute $x=1$ into $y=x^2+x+10$:
$y=(1)^2+1+10=12$ (does not match 10)

Answer:

C. $y = 5x^2 + 7x - 2$