Question 275837
f(x) = 4x2 + 4x - 3
I need help to find the intercepts, the vertex and the maximum or minimum.
y = 4x^2 + 4x - 3
The y intercept occurs when x=0
y = 4(0) + 4(0) - 3
y = -3 is the y intercept
:
You can use the quadratic formula to find the x intercepts
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
In this equation a=4, b=4, c=-3
{{{x = (-4 +- sqrt(4^2-4*4*-3 ))/(2*4) }}}
:
{{{x = (-4 +- sqrt(16-(-48) ))/8 }}}
:
{{{x = (-4 +- sqrt(16+48))/8 }}}
:
{{{x = (-4 +- sqrt(64 ))/8 }}}
Two solutions
{{{x = (-4 + 8)/8 }}}
x = {{{4/8}}}
x = .5
and
{{{x = (-4 - 8)/8 }}}
x = {{{-12/8}}}
x = -1.5
:
The x intercepts: x=.5, x=-1.5
:
Find the vertex,
first find the axis of symmetry using the formula x = -b/(2a)
x = {{{(-4)/(2*4)}}}
x = -.5 
The vertex occurs at x=-.5
:
Substitute that in the original equation for find y
y = 4(-.5^2) + 4(-.5) - 3
y = 4(.25) -2 - 3
y = +1 - 2 - 3
y = -4
:
Vertex: x=-.5,y=-4; and it is a minimum
:
Looks like this
{{{ graph( 300, 200, -4, 4, -6, 4, 4x^2+4x-3) }}}
:
The intercepts and vertex should be apparent when you see it on this graph