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:

$-3x^{2}+24x-51$

Step-by-step explanation:

we have that the form of the parabola's equation is

$ax^{2}+bx+c$

an also we have

$a(4)^{2}+b(4)+c=-3\\a(5)^{2}+b(5)+c=-6$

and for the vertex in (4,-3)

$x=-\frac{b}{2a}$

$4=-\frac{b}{2a}\\b=-8a$      (1)

if we subtract the first equation to the second equation we can obtain a 2x2 system equation

$9a+b=-3\\b=-3-9a$   (2)

and by taking the equations (1) and (2)

$-8a=-3-9a\\a=-3$

hence, for b we have

$b=-8(a)=-8(-3)=24$

and to compute c we can use

$a(4)^{2}+b(4)+c=-3\\(-3)(16)+(24)(4)+c=-3\\c=-51$

Finally we have that the parabola is

$-3x^{2}+24x-51$

I hope this is useful for you

regards