Question

select the correct answer.
a parabola passes through the points (-3,0), (-2,3), and (-1,4). what function does it represent?
a. f(x) = -x² + x + 3
b. f(x) = -2x² - x + 3
c. f(x) = -x² - 2x + 3
d. f(x) = 2x² - x - 3

Explanation:

Step1: Test point (-3,0) in option A

Substitute \( x = -3 \) into \( f(x) = -x^2 + x + 3 \):
\( f(-3)=-(-3)^2+(-3)+3=-9 - 3 + 3=-9
eq0 \). So A is wrong.

Step2: Test point (-3,0) in option B

Substitute \( x = -3 \) into \( f(x)=-2x^2 - x + 3 \):
\( f(-3)=-2\times(-3)^2-(-3)+3=-18 + 3 + 3=-12
eq0 \). So B is wrong.

Step3: Test point (-3,0) in option C

Substitute \( x = -3 \) into \( f(x)=-x^2 - 2x + 3 \):
\( f(-3)=-(-3)^2-2\times(-3)+3=-9 + 6 + 3=0 \). Now test point (-2,3):
Substitute \( x = -2 \) into \( f(x)=-x^2 - 2x + 3 \):
\( f(-2)=-(-2)^2-2\times(-2)+3=-4 + 4 + 3=3 \). Test point (-1,4):
Substitute \( x = -1 \) into \( f(x)=-x^2 - 2x + 3 \):
\( f(-1)=-(-1)^2-2\times(-1)+3=-1 + 2 + 3=4 \). All points satisfy.

Step4: Test point (-3,0) in option D (optional)

Substitute \( x = -3 \) into \( f(x)=2x^2 - x - 3 \):
\( f(-3)=2\times(-3)^2-(-3)-3=18 + 3 - 3=18
eq0 \). So D is wrong.

Answer:

C. \( f(x)=-x^2 - 2x + 3 \)