Question

Consider the parabola given by the equation:

f
(
x
)
=
4
x
2
+
6
x
−
12


Find the following for this parabola:

A) The vertex:


B) The vertical intercept is the point


C) Find the coordinates of the two
x
intercepts of the parabola and write them as a list, separated by commas:

Answer 1

Hi,

Explanation:

`f(x)=y=4x^2+6x-12\\=(2x)^2+2*2x*\drac{3}{2} +(9)/(4) -12-(9)/(4)\\=(2x+(3)/(2) )^2-(57)/(4) \\\\`

a) vertex: (-3/2,-57/4)

b) vertical intercept:

x=0, f(0)=4*0²+6*x-12=-12

=> (0,-12)

c) horizontal intercepts

y=0

`(2x+(3)/(2) )^2-(57)/(4) =0\\\\2x+(3)/(2)=(√(57) )/(2) \ or\ 2x+(3)/(2)=-(√(57) )/(2) \\\\2x=-(3)/(2)+(√(57) )/(2) \ or\ 2x=-(3)/(2)-(√(57) )/(2) \\\\x=(-3+√(57))/(4) \ or\ x=(-3-√(57))/(4)\\\\intercepts=\{(-3+√(57))/(4) \ ,\ (-3-√(57))/(4)\}\\`