SOLUTION: Give one (1) illustrative example for each concept on transforming quadratic functions. Write your answer in general form y = ax^2+bx+c and its equivalent vertex form y=a(x-h)^2+k

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Give one (1) illustrative example for each concept on transforming quadratic functions. Write your answer in general form y = ax^2+bx+c and its equivalent vertex form y=a(x-h)^2+k      Log On


   

Question 1186198: Give one (1) illustrative example for each concept on transforming quadratic functions. Write your answer in general form y = ax^2+bx+c and its equivalent
vertex form y=a(x-h)^2+k.
Concepts
- Transforming a quadratic function in the form y=ax^2+ bx+c into the form y=a(x-h)^2 by completing the square.
WHAT IS THE ILLUSTRATIVE EXAMPLES?
- Transforming a quadratic function in the form y=ax²+bx+c into the form y=a(x-h) ²+ k by applying the formula: h=-b/2a and k = 4ac-b²/4a.
WHAT IS THE ILLUSTRATIVE EXAMPLES?
- Transforming a quadratic function in the form y=a(x-h)² + k into the formy ax^2+ bx+c.
WHAT IS THE ILLUSTRATIVE EXAMPLES?​
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

- Transforming a quadratic function in the form y=ax%5E2%2B+bx+%2Bc into the form y=a%28x-h%29%5E2+ by completing the square:

y+=+2x%5E2+-+4x+%2B+5
y+=+%282x%5E2+-+4x%29%2B+5
y+=+2%28x%5E2+-+2x%29%2B+5
y+=+2%28x%5E2+-+2x%2Bb%5E2%29-2b%5E2%2B+5.......in this case b=-1
y+=+2%28x%5E2+-+2x%2B%28-1%29%5E2%29-2%28-1%29%5E2%2B+5
y+=+2%28x-1%29%5E2-2%2B+5
y+=+2%28x-1%29%5E2%2B+3

-Transforming a quadratic function in the form y=ax%5E2%2Bbx%2Bc+into the form y=a%28x-h%29+%5E2%2B+k+by applying the formula: h=-b%2F%282a%29+and k+=+%284ac-b%5E2%29%2F%284a%29
y+=+x%5E2+-+6x+%2B+7+-> a=1,+b=-6, c=7
h=-%28-6%29%2F%282%2A1%29+
h=6%2F2+
h=3
k+=+%284%2A1%2A7-%28-6%29%5E2%29%2F%284%2A1%29
k+=+%2828-36%29%2F4
k+=-8%2F4
k+=+-2
=>y=a%28x-h%29+%5E2%2B+k+
y=1%28x-3%29+%5E2-2+
y=%28x-3%29+%5E2-2+

- Transforming a quadratic function in the form y=a%28x-h%29%5E2+%2B+k into the form y=ax%5E2%2B+bx%2Bc.
y=-3%28x-2%29%5E2-5
y=-3%28x%5E2-4x%2B4%29-5
y=-3x%5E2%2B12x-12-5
y=-3x%5E2%2B12x-17