SOLUTION: Find the vertex and intercepts for each quadratic function, and sketch its graph y = x^2 + 4x y = x^2 + 2x - 24 I have not clue what formula to use. HELP! Thanks i

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find the vertex and intercepts for each quadratic function, and sketch its graph y = x^2 + 4x y = x^2 + 2x - 24 I have not clue what formula to use. HELP! Thanks i      Log On


   

Question 9425: Find the vertex and intercepts for each quadratic function, and sketch its graph

y = x^2 + 4x

y = x^2 + 2x - 24

I have not clue what formula to use. HELP! Thanks in advance.
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
y = x^2 + 4x
y = x(x+4) = 0
X-intercepts at x=0 and x= -4

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B4x%2B0+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%284%29%5E2-4%2A1%2A0=16.

Discriminant d=16 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+16+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+16+%29%29%2F2%5C1+=+0
x%5B2%5D+=+%28-%284%29-sqrt%28+16+%29%29%2F2%5C1+=+-4

Quadratic expression 1x%5E2%2B4x%2B0 can be factored:
1x%5E2%2B4x%2B0+=+1%28x-0%29%2A%28x--4%29
Again, the answer is: 0, -4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B0+%29



y = x^2 + 2x - 24
Y = (x+ 6)(x -4)
X-intercepts at x= -6 and x= 4

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-24+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%282%29%5E2-4%2A1%2A-24=100.

Discriminant d=100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+100+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+100+%29%29%2F2%5C1+=+4
x%5B2%5D+=+%28-%282%29-sqrt%28+100+%29%29%2F2%5C1+=+-6

Quadratic expression 1x%5E2%2B2x%2B-24 can be factored:
1x%5E2%2B2x%2B-24+=+1%28x-4%29%2A%28x--6%29
Again, the answer is: 4, -6. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-24+%29



R^2 at SCC with help from "i from Chicago"