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?

A.3  B.2  C.-3. D.-2

Answer 1

formula for parabola is y = a(x - h)^2 + k where vertex is (h,k)

Given: vertex is (4, -3) plus this into the equation h = 4 and k = -3

y = a(x - 4)^2 + -3

Given: x-value is 5 the y-value is -6 plug these numbers in to solve for a.

-6 = a (5 - 4) ^2 +-3
-6 = a (1)^2 + -3 add 3 to both sides
-6 + 3 = a (1) +-3 + 3
-3 = a
the coefficient "a" is -3

Enjoy! :-)

Answer 2

when you mention the coefient of the squared term, I assume you mean the value of a in y=a(x-h)²+k and not the value of a in y=ax²+bx+c (actually they are the same)

so

using vertex form
y=a(x-h)²+k
vertex is (h,k)
so, given vertex of (4,-3)
y=a(x-4)²-3

also, a point is when x=5, y=-6 so (5,-6) is a point
sub to find a
-6=a(5-4)²-3
-6=a(1)²-3
-6=a-3
-3=a

so the answer is C