SOLUTION: how do you turn the vertex form; y=4(3x-1)^2+8 back into standard form?
Algebra.Com
Question 1204096: how do you turn the vertex form; y=4(3x-1)^2+8 back into standard form?
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!
Answer: y = 36x^2-24x+12
Work Shown
y = 4(3x-1)^2+8
y = 4(3x-1)(3x-1)+8
y = 4(9x^2-6x+1)+8 ....... use the FOIL rule or box method
y = 36x^2-24x+4+8 ....... distribute
y = 36x^2-24x+12
We have 4(3x-1)^2+8 expand and simplify to 36x^2-24x+12
Therefore, 4(3x-1)^2+8 = 36x^2-24x+12 is an identity.
It is a true equation for all real numbers x.
Ways to verify:- Graph y = 4(3x-1)^2+8 and y = 36x^2-24x+12 to notice they produce the exact same parabola (i.e. they pass through the exact same set of points). Desmos and GeoGebra are two graphing options I recommend. Graphing calculators such as a TI83 or TI84 work as well.
- Make a table of values comparing each quadratic. The tables should be identical when using the same input x values.
- Use a computer algebra system (CAS) to verify that 4(3x-1)^2+8 turns into 36x^2-24x+12. GeoGebra is one example of a CAS. WolframAlpha is another.
Extra side notes:- Standard form is y = ax^2 + bx + c
- Technically the given equation y = 4(3x-1)^2+8 is NOT in vertex form because vertex form has the template y = a(x-h)^2+k
- The vertex form for this particular equation is y = 36(x - 1/3)^2 + 8
- The vertex is located at (1/3, 8)
RELATED QUESTIONS
How do you convert the vertex form y=4(3x-1)^2+8 back into standard... (answered by greenestamps,josgarithmetic)
How do you turn the equation h=-5t^2+20t+105 into vertex form? Thank you (answered by ewatrrr)
How do you turn slope intercept into standard form?
(answered by checkley77)
How would I turn the point slope form linear equation, y-3=3(X+1), into standard form?... (answered by rothauserc)
how do i turn this problem into standard form... (answered by elima)
How can you turn y=-5/7x-8 into standard form... (answered by josmiceli)
how do i turn this equation into standard form... (answered by checkley77)
How do you the parabola y=4x^2-12x+5 into vertex form and intercept... (answered by Fombitz)
How do you turn 6y = -3x + 30 into y=mx+b... (answered by MathLover1,josgarithmetic,Alan3354)