From Factored To Standard Form - Math Education Page printable pdf download

From Factored To Standard Form - Math Education Page

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From Factored to Standard Form

This is the equation of a parabola, in standard form: y = ax

+ bx + c. The important

points of the function are sometimes more difficult to see in this form, but they can be

found using your knowledge of factored form.

0. Recall:

Factored Form of a quadratic function looks like

y = a(x – p)(x – q)

In terms of a, p, and q,

The x-intercepts (the roots) are:

The y-intercept is:

The x-coordinate of the vertex is:

1. Given the function y = 2x

– 2x – 24,

a. Find the roots (by factoring).

b. Find the y-intercept.

c. Find the coordinates of the vertex.

d. Find the sum and product of the roots. (You will see why this is useful later.)

2. Take the equation y = a (x – p) (x – q), and distribute, so as to write it in standard

form. [Hint: this is a two-step process. First multiply a(x – p). Then multiply the

product by (x – q).]

3. Write formulas for b and c in terms of a, p, and q.

4. Generalize for any quadratic in standard form:

Standard form of a quadratic function looks like:

y = ax

+ bx + c

In terms of a, b, and

The y-intercept is:

The sum of the roots is:

The product of the roots is:

The x-coordinate of the vertex is:

Henri Picciotto – Urban School of San Francisco

From Factored To Standard Form - Math Education Page