`y = 3x^2 -8x + 4` Write the quadratic in intercept form and give the function's zeros.

Textbook Question

Chapter 5, 5.2 - Problem 21 - McDougal Littell Algebra 2 (1st Edition, Ron Larson).
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atyourservice | Student, Grade 11 | (Level 3) Valedictorian

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We can solve this using the AC factoring method:

`3x^2 - 8x + 4`

Multiply a by c

3 x 4 = 12

Find factors of 12 that add up to b (-8)

these numbers will be -6 and -2, plug these in as b

`3x^2 - 6x - 2x + 4`

now group:

`(3x^2 - 6x) (-2x + 4)`

Factor out the greatest common factors:

3x (x - 2 ) - 2 (x - 2)

Put the numbers outside in a parentheses together :

(x - 2) (3x - 2)

x = 2  x =` 2/3 ` will be the zeros

The intercept form is known as y = a (x-p)(x-q)

the points where the graph crosses the x axis (The zeros) are the p and q

`y = a (x-2)(x-2/3)`

 Now we need to find a, and we can do that by graphing the equation and picking any point that isn't one of the zeros.
 
we can see that the graph crosses y at (0,4) we can use this coordinate to plug in and find a.
 
` 4 = a (0-2) ( 0 -2/3)`
 
`4 = a (-2) (-2/3)`
`4 = a (4/3)`
3 = a
so the intercept form is:
 

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