From Factored To Standard Form - Math Education Page

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From Factored to Standard Form
2
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:
2
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:
2
y = ax
+ bx + c
In terms of a, b, and
c,
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

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