write the equation of the parabola shown in the graph. write your answer in standard form, y = ax^2 + bx +…

write the equation of the parabola shown in the graph. write your answer in standard form, y = ax^2 + bx + c, where a, b, and c are integers, decimals, or simplified fractions.

write the equation of the parabola shown in the graph. write your answer in standard form, y = ax^2 + bx + c, where a, b, and c are integers, decimals, or simplified fractions.

Answer

Explanation:

Step1: Use factored - form of parabola

The x - intercepts are $x=-4$ and $x = 1$. So the factored form of the parabola is $y=a(x + 4)(x - 1)$.

Step2: Substitute a point to find a

Substitute the point $(-3,4)$ into $y=a(x + 4)(x - 1)$. We get $4=a(-3 + 4)(-3 - 1)$. Simplify the right - hand side: $4=a(1)(-4)$, so $a=-1$.

Step3: Expand to standard form

Expand $y=-(x + 4)(x - 1)$. First, $(x + 4)(x - 1)=x^{2}-x+4x-4=x^{2}+3x - 4$. Then $y=-x^{2}-3x + 4$.

Answer:

$y=-x^{2}-3x + 4$