SOLUTION: Write the eqation of the parabola y=x^2+2x-10 in standard form. a. y+1=(x+1)^2 c. y+10=(x+1)^2 b. y+1=(x+1)^2 d. y+11=(x+1)^2

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Write the eqation of the parabola y=x^2+2x-10 in standard form. a. y+1=(x+1)^2 c. y+10=(x+1)^2 b. y+1=(x+1)^2 d. y+11=(x+1)^2      Log On


   

Question 698650: Write the eqation of the parabola y=x^2+2x-10 in standard form.
a. y+1=(x+1)^2 c. y+10=(x+1)^2
b. y+1=(x+1)^2 d. y+11=(x+1)^2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

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


y=1+x%5E2%2B2+x-10 Start with the given equation



y%2B10=1+x%5E2%2B2+x Add 10 to both sides



y%2B10=1%28x%5E2%2B2x%29 Factor out the leading coefficient 1



Take half of the x coefficient 2 to get 1 (ie %281%2F2%29%282%29=1).


Now square 1 to get 1 (ie %281%29%5E2=%281%29%281%29=1)





y%2B10=1%28x%5E2%2B2x%2B1-1%29 Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of 1 does not change the equation




y%2B10=1%28%28x%2B1%29%5E2-1%29 Now factor x%5E2%2B2x%2B1 to get %28x%2B1%29%5E2



y%2B10=1%28x%2B1%29%5E2-1%281%29 Distribute



y%2B10=1%28x%2B1%29%5E2-1 Multiply



y=1%28x%2B1%29%5E2-1-10 Now add %2B10 to both sides to isolate y



y=1%28x%2B1%29%5E2-11 Combine like terms




Now the quadratic is in vertex form y=a%28x-h%29%5E2%2Bk where a=1, h=-1, and k=-11. Remember (h,k) is the vertex and "a" is the stretch/compression factor.




Check:


Notice if we graph the original equation y=1x%5E2%2B2x-10 we get:


graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C1x%5E2%2B2x-10%29 Graph of y=1x%5E2%2B2x-10. Notice how the vertex is (-1,-11).



Notice if we graph the final equation y=1%28x%2B1%29%5E2-11 we get:


graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C1%28x%2B1%29%5E2-11%29 Graph of y=1%28x%2B1%29%5E2-11. Notice how the vertex is also (-1,-11).



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






the answer is: d. y%2B11=%28x%2B1%29%5E2