SOLUTION: Find the axis of symmetry... 1. y=-x^2+4x+2 2. y=x^2+x+1 Find the x-intercepts... 1.y=x^2+2x-8 2. y=x^2-5x-10

Question 86122: Find the axis of symmetry...
1. y=-x^2+4x+2
2. y=x^2+x+1
Find the x-intercepts...
1.y=x^2+2x-8
2. y=x^2-5x-10
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
1.

Solved by pluggable solver: Completing the Square to Get a Quadratic into Vertex Form

Start with the given equation

Subtract from both sides

Factor out the leading coefficient

Take half of the x coefficient to get (ie ).

Now square to get (ie )

Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of does not change the equation

Now factor to get

Distribute

Multiply

Now add to both sides to isolate y

Combine like terms

Now the quadratic is in vertex form where , , and . Remember (h,k) is the vertex and "a" is the stretch/compression factor.

Check:

Notice if we graph the original equation we get:

Graph of . Notice how the vertex is (,).

Notice if we graph the final equation we get:

Graph of . Notice how the vertex is also (,).

So if these two equations were graphed on the same coordinate plane, one would overlap another perfectly. So this visually verifies our answer.

Solved by pluggable solver: Completing the Square to Get a Quadratic into Vertex Form

We can find the x-intercepts by the quadratic formula
1.
Starting with the general quadratic

the general form of the quadratic equation is:

So lets solve

Plug in a=1, b=2, and c=-8

Square 2 to get 4

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our solutions are:
or

Notice when we graph we get:

and we can see that the roots are and . This verifies our answer

2.
Starting with the general quadratic

the general form of the quadratic equation is:

So lets solve

Plug in a=1, b=-5, and c=-10

Square -5 to get 25

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Which approximate to

or

So our solutions are:
or

Notice when we graph we get:

when we use the root finder feature on our calculator, we find that and .So this verifies our answer
RELATED QUESTIONS
Y=1/2x^2+5x+1 find the vertex, x intercepts and axis of symmetry (answered by Boreal)

Find the axis of symmetry.... (answered by stanbon)

Find the axis of symmetry. y = �x^2 � 8x +... (answered by jim_thompson5910)

1. 5(x - 2)^2=3 2. Find the x-intercepts. y = x^2 + 3x - 8 3. Find the axis of... (answered by stanbon)

Find the axis of symmetry. y = x^2 + 5x � 7 (answered by stanbon)

Find the axis of symmetry. y = �x^2 + 4x � 6 (answered by jim_thompson5910)

Find vertex,axis of symmetry, y-intercept and x-intercepts... (answered by Fombitz)

Find the x-intercepts y=x^2+4x-1 (answered by checkley77)