(multiply by the LCD
which is 15y(y + 1))
(use quadratic formula–I always write it
or y = 5
Since neither y = 9 nor y = 5 makes the LCD zero , these
are both solutions.
• The hypotenuse in a right triangle is the side opposite the 90 degree angle in
• Pythagorean theorem: a2 = b2 + c2, where a is
the length of the hypotenuse in a right triangle and b and c are the
lengths of the other two sides.
• For a quadratic y = f(x) = ax2 + bx + c, we have
• x-intercepts: determine these by using the quadratic formula
NOTE: If b2 − 4ac < 0 then there are no x-intercepts (they are not
real numbers ).
How to remember this: The x-coordinate of the vertex will
be right in the middle of the two x-intercepts, even if
the x-intercepts are not real numbers!
• y-intercept: evaluate at x = 0, so figure out what f(0)
• The function opens up if a > 0, and opens down if a < 0.
Example Sketch the parabola y = 5x2 + 4x − 12. Label the
vertex, y-intercept, and any x-intercepts on your sketch.
To get the sketch of a quadratic, we should do four things:
• Determine if it opens up or down,
• Determine the vertex,
• Determine any x-intercepts (if they exist),
• Determine the y-intercept.
A quadratic opens up if a > 0, and opens down if a < 0. Since a = 5 in this
case, this quadratic opens up.
To get the vertex, identity a = 5, b = 4, and c = −12. Then the vertex is
The vertex is at
To get the x-intercepts, use the quadratic formula:
To get the y-intercept, evaluate f(0):
y = f(0) = 5(0)2 + 4(0) − 12 = −12
You can now put this all together to get the sketch:
Start solving your Algebra Problems
in next 5 minutes!
Download (and optional CD)
Click to Buy Now:
2Checkout.com is an authorized reseller
of goods provided by Sofmath
Attention: We are
currently running a special promotional offer
for Algebra-Answer.com visitors -- if you order
Algebra Helper by midnight of
you will pay only $39.99
instead of our regular price of $74.99 -- this is $35 in
savings ! In order to take advantage of this
offer, you need to order by clicking on one of
the buttons on the left, not through our regular
If you order now you will also receive 30 minute live session from tutor.com for a 1$!
You Will Learn Algebra Better - Guaranteed!
Just take a look how incredibly simple Algebra Helper is:
: Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:
Step 2 :
Let Algebra Helper solve it:
Step 3 : Ask for an explanation for the steps you don't understand:
Algebra Helper can solve problems in all the following areas:
simplification of algebraic expressions (operations
with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots
(radicals), absolute values)