Question

Finding the Equation of a Parabola In Exercises $49 - 54 ,$ find the equation of the parabola $$y = a x ^ { 2 } + b x + c$$ that passes through the points. To verify your result, use a graphing utility to plot the points and graph the parabola. $$( 0,0 ) , ( 2 , - 2 ) , ( 4,0 )$$

          Finding the Equation of a Parabola In Exercises
$49 - 54 ,$ find the equation of the parabola
$$y = a x ^ { 2 } + b x + c$$
that passes through the points. To verify your result, use
a graphing utility to plot the points and graph the
parabola.

$$( 0,0 ) , ( 2 , - 2 ) , ( 4,0 )$$

Added by Scott F.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Emily Anderson

Step 1

When $x=0$, $y=0$, so we have $0=a(0)^2+b(0)+c$, which simplifies to $c=0$. When $x=2$, $y=-2$, so we have $-2=a(2)^2+b(2)+c$, which simplifies to $4a+2b-2=0$. When $x=4$, $y=0$, so we have $0=a(4)^2+b(4)+c$, which simplifies to $16a+4b=0$. So we have the Show more…

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Finding the Equation of a Parabola In Exercises $49 - 54 ,$ find the equation of the parabola $$y = a x ^ { 2 } + b x + c$$ that passes through the points. To verify your result, use a graphing utility to plot the points and graph the parabola. $$( 0,0 ) , ( 2 , - 2 ) , ( 4,0 )$$