Question

Sandra wrote p(x) = 30x + 5x2 in vertex form. Her work is below.

1. p(x) = 5x2 + 30x

2. p(x) = 5(x2 + 6x)

3. (six-halves) squared = 9;

4. p(x) = 5(x2 + 6x + 9) – 5(9)

5. p(x) = 5(x + 3)2 – 45

Describe Sandra’s function.

Answer 1

Answer:

p(x) = 5(x + 3)² - 45

Step-by-step explanation:

Sandra wrote the function as p(x) = 30x + 5x².

So, this is a formula of a parabola, and this we have to convert into vertex form.

Now, rearranging the function we get

p(x) = 5(x² + 6x)

⇒ p(x) = 5(x² + 6x + 9) - 45

⇒ p(x) = 5(x + 3)² - 45

So, this is the vertex form and the vertex of the parabola is (-3,-45).

We know the formula of a parabola having vertex at (m,n) and axis parallel to positive y-axis is given by

(x - m)² = 4a(y - n)

⇒ $y = \frac{1}{4a} (x - m)^{2} + n$ (Answer)