Question

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 parabola's equation

Answer 1

Answer:

Step-by-step explanation:

The work form of this upside down parabola is

$y=-|a|(x-h)^2+k$

It's VERY important that you remember that the negative value there in front of the absolute value of a just means that the parabola is upside down. a itself will not be negative (and we know that because of the absolute value symbols there!). Filling in the x, y, h, and k values we were given allows us to solve for the |a|:

$-6=-|a|(5-4)^2-3$ and

$-6=-|a|(1)^2-3$ and

$-6=-|a|1-3$ and

$-6=-|a|(-2)$ and

3 = -|a|

Again, the negative simply tells us the parabola is upside down, so the absolute value of a = 3, choice c.