Question

2.4.4 quiz: parabolas with vertices not at the origin
the vertex of this parabola is at (4, -3). when the x - value is 5, the y - value is -6. what is the coefficient of the squared expression in the parabolas equation?
a. 3
b. - 3
c. 2
d. - 2

Explanation:

Step1: Write the vertex - form of the parabola equation

The vertex - form of a parabola is $y=a(x - h)^2+k$, where $(h,k)$ is the vertex of the parabola. Given that the vertex is $(4,-3)$, the equation of the parabola is $y=a(x - 4)^2-3$.

Step2: Substitute the given point into the equation

We know that when $x = 5$, $y=-6$. Substitute these values into the equation $y=a(x - 4)^2-3$:
$-6=a(5 - 4)^2-3$.

Step3: Solve for $a$

First, simplify the right - hand side of the equation:
$-6=a(1)^2-3$, which is $-6=a - 3$.
Add 3 to both sides of the equation: $a=-6 + 3=-3$.

Answer:

B. -3