SOLUTION: f(x)4x2 + 4x - 3 I need help to find the intercepts, the vertex and the maximun or minimun. I know I need to use the quadratic formula, but I don't know how to apply it to find t

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: f(x)4x2 + 4x - 3 I need help to find the intercepts, the vertex and the maximun or minimun. I know I need to use the quadratic formula, but I don't know how to apply it to find t      Log On


   

Question 275837: f(x)4x2 + 4x - 3
I need help to find the intercepts, the vertex and the maximun or minimun.
I know I need to use the quadratic formula, but I don't know how to apply it to find these three points.
Thank you for your help.
Martha
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this equation a=4, b=4, c=-3
x+=+%28-4+%2B-+sqrt%284%5E2-4%2A4%2A-3+%29%29%2F%282%2A4%29+
:
x+=+%28-4+%2B-+sqrt%2816-%28-48%29+%29%29%2F8+
:
x+=+%28-4+%2B-+sqrt%2816%2B48%29%29%2F8+
:
x+=+%28-4+%2B-+sqrt%2864+%29%29%2F8+
Two solutions
x+=+%28-4+%2B+8%29%2F8+
x = 4%2F8
x = .5
and
x+=+%28-4+-+8%29%2F8+
x = -12%2F8
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 = %28-4%29%2F%282%2A4%29
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%28+300%2C+200%2C+-4%2C+4%2C+-6%2C+4%2C+4x%5E2%2B4x-3%29+
:
The intercepts and vertex should be apparent when you see it on this graph