SOLUTION: y = − x^2 − 8 x − 14 Find the coordinates of the vertex these intercepts occur at? x= x= Thanks

Algebra ->  Equations -> SOLUTION: y = − x^2 − 8 x − 14 Find the coordinates of the vertex these intercepts occur at? x= x= Thanks      Log On


   

Question 948104: y = − x^2 − 8 x − 14
Find the coordinates of the vertex
these intercepts occur at?
x=
x=
Thanks
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
The vertex form of a parabola's equation is generally expressed as:
y+=+a%28x-h%29%5E2%2Bk where (h,k) is the vertex
so, write your equation in vertex form:
y+=+-x%5E2+-8x+-14

y+=+-%28x%5E2+%2B8x%29+-14...complete square
y+=+%28-1%29%28x%5E2+%2B8x%2B_%29-%28-1%29%2A_+-14
y+=+-%28x%5E2+%2B8x%2B4%5E2%29%2B1%2A4%5E2+-14
y+=+-%28x%2B4%29%5E2+%2B16+-14
y+=+-%28x%2B4%29%5E2%2B2
(-4,2) is the vertex
intercepts:
0=+-x%5E2+-8x+-14...multiply by -1%7D%7D%0D%0A%0D%0A%7B%7B%7Bx%5E2%2B8x+%2B14=0 ...use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-8+%2B-+sqrt%28+8%5E2-4%2A1%2A14+%29%29%2F%282%2A1%29+
x+=+%28-8+%2B-+sqrt%28+64-56+%29%29%2F2+
x+=+%28-8+%2B-+sqrt%28+8+%29%29%2F2+
x+=+%28-8+%2B-+2.8%29%2F2+
x+=+%28-4+%2B-+1.4%29+
solutions:
x+=+-4+%2B+1.4+
x+=-2.6+
or
x+=+-4-+1.4+
x+=-5.4+
so, x-intercepts are at:
(-2.6,0)
and
(-5.4,0)