SOLUTION: Find the x intercepts for the parabola y = x2 – 6x + 5. Find the vertex of the parabola y = - 2x2 + 8x + 4

Algebra.Com
Question 212102: Find the x intercepts for the parabola y = x2 – 6x + 5.
Find the vertex of the parabola y = - 2x2 + 8x + 4


Answer by drj(1380)   (Show Source): You can put this solution on YOUR website!
Find the x intercepts for the parabola y = x2 – 6x + 5.
Step 1. For this problem y=0 since we want x-intercepts.

Step 2. Use quadratic formula:

where a=1, b=-6 and c= 5
Step 3. The following steps shows how to solve the above equation in Step 2 where you will find x=1 and x=5. Note the parabola intercepts x-axis when y=6 at these points.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=16 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 5, 1. Here's your graph:





Problem: Find the vertex of the parabola y = - 2x2 + 8x + 4



Step 1. Graph is shown below and the vertex is at (2,12)
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=96 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: -0.449489742783178, 4.44948974278318. Here's your graph:



For Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra.


RELATED QUESTIONS

a Find the x intercepts for the parabola y = x2 – 6x + 5. b Find the vertex of the... (answered by jojo14344)
Find the vertex of the parabola y= -2x2 + 12x -... (answered by oberobic)
Find the vertex of the parabola:... (answered by user_dude2008)
find vertex of the parabola y=x^2-8x-5 vertex... (answered by drj)
find the vertex of the parabola... (answered by lynnlo)
Find the x-intercepts of the parabola with vertex (4,-1)and y- intercept... (answered by ewatrrr)
Find the x-intercepts of the parabola with vertex (4,-1) and y-intercept... (answered by Fombitz)
Find the vertex and intercepts of the parabola. y = -3x^2 +... (answered by amoresroy)
parabola,x^2 +6x -y +11 =0 find the vertex,focus and directrix of the... (answered by lwsshak3)