Answer:
Step-by-step explanation:
x^2-1=0
Add 1 to both sides of the equation.
x^2=
1
Take the square root of both sides of the equation to eliminate the exponent on the left side.
x
=
±
√
1
Any root of 1 is x
=
±
1
First, use the positive value of the ±
to find the first solution.
x=
1
Next, use the negative value of the ±
to find the second solution.
x
=
−
1
The complete solution is the result of both the positive and negative portions of the solution.
x
=
1
,
−
1
Yes. the factors of 11 are 1, and 11.
The number y, decreased by 12
Discussion
1. Put brackets around the first two terms
y = (-x^2 + 6x) + 5
2. Take out the common factor of -1
y = -(x^2 - 6x) + 5
3. Inside the brackets, take 1/2 of - 6 and square it
y = -(x^2 - 6x + ( - 6 / 2)^2 ) + 5
y = -(x^2 - 6x + (- 3)^2 ) ) + 5
y = -(x^2 - 6x + 9 ) + 5
Note: Step 3 is very long. Make sure you work your way through it
4. You have added 9 inside the brackets. <em><u>It is actually - 9. So add 9 outside to balance the equation out. </u></em> This is the key step. Make sure you understand it.
y = - (x^2 - 6x + 9) + 5 + 9
5. Express the brackets as a square.
y = - (x + 3)^2 + 14
Discussion
The equation is now in vertex form. The minus tells you that the equation is a maximum. The maximum is located at ( - 3, 14 )
A graph follows to show the results.