Question

Transforming quadratic graphs

Answer 1

f(x) = 3(x - 2)² + 4

OR

f(x) = 3x² - 12x + 16

Explanation:

Vertex form of a parabola:

• y = a(x - h)² + k

Standard form of a parabola:

• y = ax² + bx + c

Let's find the vertex of this parabola.

• (h, k) → (2, 4)

In order to find the a-value (vertex form), let's use another point besides the vertex on the parabola.

Using (3, 7) for (x, y), let's substitute this point and the vertex (2, 4) for (h, k) into the vertex form equation and solve for a.

• 7 = a[(3) - (2)]² + 4

Simplify using PEMDAS.

• 7 = a(1)² + 4
• 7 = a + 4

Subtract 4 from both sides.

• a = 3

Now we have (h, k) and a of the vertex form.

• y = a(x - h)² + k → y = 3(x - 2)² + 4

In order to convert from vertex to standard form, simplify the equation by FOILing.

• y = 3(x - 2)² + 4

• y = 3(x² - 4x + 4) + 4

Distribute 3 inside the parentheses.

• y = 3x² - 12x + 12 + 4

Combine like terms.

• y = 3x² - 12x + 16

Therefore, we have the answer:

Vertex form:

• f(x) = 3(x - 2)² + 4

Standard form:

• f(x) = 3x² - 12x + 16