Question

I really suck at Quadratics, can anyone of you guys help me out? :/

The equation is: f(x) = 1/3 (x-3)(x+7)

I need to find -

x intercepts

y intercept

vertex

equation in vertex form

equation in standard form


Someone please help! <3

Answer 1

@abb0t are you any good at Quadratics?

Answer 2

I think I figured out the x and y intercepts:

x intercepts - (3,0) (-7,0)
y intercept - (0,-7)
vertex - ?

How do I go from intercept form to standard and vertex form though? :( ughhhhh

Answer 3

Two solutions were found :

x = -7
x = 3
Rearrange :

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

0-(1/3*(x-3)*(x+7))=0
Step by step solution :
Step 1 :

(x-3)•(x+7)
Simplify 0 - ———————————
3

Equation at the end of step 1 :

(3 - x) • (x + 7)
————————————————— = 0
3

Step 2 :

(3-x)•(x+7)
Solve ——————————— = 0
3

When a fraction equals zero :

2.1 When a fraction equals zero ...

Where a fraction equals zero, its nominator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

(3-x)•(x+7)
——————————— • 3 = 0 • 3
3

Now, on the left hand side, the 3 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
(3-x) • (x+7) = 0
Theory - Roots of a product :

A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solve : -x+3 = 0

Subtract 3 from both sides of the equation :
-x = -3
Multiply both sides of the equation by (-1) : x = 3


Solve : x+7 = 0

Subtract 7 from both sides of the equation :
x = -7

Answer 4

@Muzzack Wow, thanks! Do you by chance know how to go from intercept form to standard & vertex form?

Answer 5

hmm idk

Answer 6

Aww.. :( Do you know how to get the vertex? @Muzzack

Answer 7

in intercept form or standard form

Answer 8

The equation is currently in Intercept form, is that what you're asking?

Answer 9

I need to get to Standard form and then I can find Vertex form. But idk how to get Standard form :(

Answer 10

yes

Answer 11

http://www.virtualnerd.com/algebra-2/quadratics/transforming-functions/intercept-form/graph-intercept-form check this out