SOLUTION: Find the y-intercept,the equation of the axis of symmetry, and the x-coordinate of the vertex for f(x)=3x^2-12x+4. Then graph the function by making a table of values.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: Find the y-intercept,the equation of the axis of symmetry, and the x-coordinate of the vertex for f(x)=3x^2-12x+4. Then graph the function by making a table of values.       Log On


   

Question 115108: Find the y-intercept,the equation of the axis of symmetry, and the x-coordinate of the vertex for f(x)=3x^2-12x+4. Then graph the function by making a table of values.
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=3+x%5E2-12+x%2B4 Start with the given equation



y-4=3+x%5E2-12+x Subtract 4 from both sides



y-4=3%28x%5E2-4x%29 Factor out the leading coefficient 3



Take half of the x coefficient -4 to get -2 (ie %281%2F2%29%28-4%29=-2).


Now square -2 to get 4 (ie %28-2%29%5E2=%28-2%29%28-2%29=4)





y-4=3%28x%5E2-4x%2B4-4%29 Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of 4 does not change the equation




y-4=3%28%28x-2%29%5E2-4%29 Now factor x%5E2-4x%2B4 to get %28x-2%29%5E2



y-4=3%28x-2%29%5E2-3%284%29 Distribute



y-4=3%28x-2%29%5E2-12 Multiply



y=3%28x-2%29%5E2-12%2B4 Now add 4 to both sides to isolate y



y=3%28x-2%29%5E2-8 Combine like terms




Now the quadratic is in vertex form y=a%28x-h%29%5E2%2Bk where a=3, h=2, and k=-8. Remember (h,k) is the vertex and "a" is the stretch/compression factor.




Check:


Notice if we graph the original equation y=3x%5E2-12x%2B4 we get:


graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C3x%5E2-12x%2B4%29 Graph of y=3x%5E2-12x%2B4. Notice how the vertex is (2,-8).



Notice if we graph the final equation y=3%28x-2%29%5E2-8 we get:


graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C3%28x-2%29%5E2-8%29 Graph of y=3%28x-2%29%5E2-8. Notice how the vertex is also (2,-8).



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