For each of the following quadratic functions find the verte

For each of the following quadratic functions, find the vertex, the vertical intercept, and the horizontal intercepts. F(x) = 3x^2 + 6x - 9 f(x) = 2x^2 + 4x - 15

Solution

8. f(x) = 3x^2 +6x -9

a) vertex for ax^2 +bx +c is given by x = -b/2a and f(-b/2a)

x = -6/(2*3) = -1 ; f(-1) = 3 -6 -9 = -12

( -1 , -12)

b) vertical intercept : x intercept: 3x^2 +6x -9 =0

3x^2 +9x -3x -9 =0 -----> 3x(x+3) -1(x+3) =0

(3x-1)(x+3) =0 ---> x = 1/3 , -3

c) horizontal intercept: y intercept : plugx=0

f(0) = -9

So, ( 0, -9)

12, f(x) = 2x^2 +4x -5

a) vertex for ax^2 +bx +c is given by x = -b/2a and f(-b/2a

x = -4/(2*4) = -1/2

f(-1/2) = 2(1/4)+4(-1/2) -5 = 1/2 -2 -5 = 1/2 -7 = -13/2

b) b) vertical intercept : x intercept: 2x^2 +4x -15 =0

use quadratice formula: x = (-4 +/- sqrt(4^2 +15*4*2) )/4

x= 1.91 , -3.92

c) horizontal intercept : x=0

f(0) = -15

( 0, -15)