SOLUTION: Hello out there,I need some help with some problems,The first one is,Find the y-intercept of y=2^x.The next one is,Use quadratic formula to solve:5x^2+12=-6x.The third one is,Use t

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hello out there,I need some help with some problems,The first one is,Find the y-intercept of y=2^x.The next one is,Use quadratic formula to solve:5x^2+12=-6x.The third one is,Use t      Log On


   

Question 92516: Hello out there,I need some help with some problems,The first one is,Find the y-intercept of y=2^x.The next one is,Use quadratic formula to solve:5x^2+12=-6x.The third one is,Use the quadratic formula to solve:x^2+12x+11=0.The last one is,Describe how the graph of y=(x-6)^2+5 changes from the parent graph of y=x^2.Thanks for any one can help.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1.Find the y-intercept of y=2^x.
The y intercept occurs when x = 0, we know that any number to the power of 0 is equal to 1.
y = 2^0
y = 1
:
2. Use quadratic formula to solve:5x^2+12=-6x. Put into the ax^2 + bx + c = 0 format.
5x^2 + 12 = -6x
5x^2 + 6x + 12 = 0
:
a = 5; b = 6; c = 12
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
:
x+=+%28-6+%2B-+sqrt%28+6%5E2+-+4+%2A+5+%2A+12+%29%29%2F%282%2A5%29+
:
x+=+%28-6+%2B-+sqrt%28+36+-+108+%29%29%2F%2810%29+
:
You can see that the discriminant will be < 0, no real roots
:
:
3. Use the quadratic formula to solve:x^2+12x+11=0.
a = 1; b = 12; c = 11
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
:
x+=+%28-12+%2B-+sqrt%28+12%5E2+-+4+%2A+1+%2A+11+%29%29%2F%282%2A1%29+
:
x+=+%28-12+%2B-+sqrt%28+144+-+44+%29%29%2F%282%29+
:
x+=+%28-12+%2B-+sqrt%28100+%29%29%2F%282%29+
:
Two solutions:
x+=+%28-12+%2B+10%29%2F%282%29+
x+=+-2%2F2+
x = -1
and
x+=+%28-12+-10%29%2F%282%29+
x = -22/2
x = -11
:
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4.Describe how the graph of y=(x-6)^2+5 changes from the parent graph of y=x^2.
Minimum is at origin in y = x^2, minimum is at x/y coordinate 6,5 for y = (x-6)^2 + 5
: