SOLUTION: Please help me with these problems: Finding the maximum y-value on the graph of y=f(x). My problem is f(x)= -x^2+8x+7 Using quadratic formula to find any x-intercepts on gr

Question 724015: Please help me with these problems:
Finding the maximum y-value on the graph of y=f(x).
My problem is f(x)= -x^2+8x+7
Using quadratic formula to find any x-intercepts on graph of equation. My problem is y=x^2+6x-1.
and
To solve by completing the square what value should be added to each side of equation with problem x^2+16x=-4.
Thanking you in advance for your help.
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Finding the maximum y-value on the graph of y=f(x).
My problem is f(x)= -x^2+8x+7
Vertex occurs at x = -b/(2a) = -8/(2*-1) = 4
Max at f(4) = -16+32+7 = 16+7 = 23
--------------------------------------------
Using quadratic formula to find any x-intercepts on graph of equation. My problem is y=x^2+6x-1.
Let y = 0
x^2+6x-1 = 0
x = [-6+-sqrt(36-4*-1)]/2
x = [-6+-sqrt(40)]/2
x = [-3+-sqrt(10)]
-------------------------------
and
To solve by completing the square what value should be added to each side of equation with problem x^2+16x=-4.
x^2+16x+64 = -4+64
-----
(x+8)^2 = 60
x+8 = +-2sqrt(15)
x = -8+-2sqrt(15)
=====================
Cheers,
Stan H.
=====================

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
1. ...here you have parabola with , so parabola is facing and the maximum on the graph will be coordinate of the vertex
the equation is where and are and coordinate of the vertex
so, we need
...factor completely
...replace with
...group first three terms together
.......note that
...vertex form... and
so, vertex is at and the maximum on the graph is
see it on a graph:

2.
Using quadratic formula to find any on graph of equation.

...note that , , and

solutions:

and

so, are at (,) and (,)
check it on a graph:

3. complete the square

...replace with
...group first three terms together
....note that is square of a sum

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