SOLUTION: Thank you in advance for helping me with this. f(x)= {{{2x^2+3x-1}}} I need to graph this quadratic funtion by completing the square. I figured out the vertix as -17/8,-3/4 I

Algebra ->  Graphs -> SOLUTION: Thank you in advance for helping me with this. f(x)= {{{2x^2+3x-1}}} I need to graph this quadratic funtion by completing the square. I figured out the vertix as -17/8,-3/4 I      Log On


   

Question 175375This question is from textbook college algebras
: Thank you in advance for helping me with this.
f(x)= 2x%5E2%2B3x-1 I need to graph this quadratic funtion by completing the square. I figured out the vertix as -17/8,-3/4 I am stuck on figuring out the two other points. I need help, thank you This question is from textbook college algebras

Answer by EMStelley(208) About Me  (Show Source):
You can put this solution on YOUR website!
First, let's complete the square.
f(x) = 2x%5E2+%2B+3x+-+1 = 2%28x%5E2+%2B+%283%2F2%29x%29+-+1
=2%28x%5E2+%2B+%283%2F2%29x+%2B+%283%2F4%29%5E2%29+-+1+-+2%283%2F4%29%5E2
=2%28x+%2B+%283%2F4%29%29%5E2+-+1+-+%289%2F8%29
=2%28x+%2B+%283%2F4%29%29%5E2+-+%2817%2F8%29
This tells us that the vertex of the parabola is (-3/4, -17/8), which is backwards from what you stated in the problem. When you say that you are stuck figuring out the other two points, I assume you are referencing the x and y intercepts. The y intercept is obtained by setting x to 0 in the original problem. So f(0) = -1 means the y intercept is (0, -1). In order to find the x intercepts, you set y = 0, and this is easier using the form above (found by completing the square).
So
0 = 2%28x+%2B+%283%2F4%29%29%5E2+-+%2817%2F8%29
17/8 = 2%28x+%2B+%283%2F4%29%29%5E2
17/16 = %28x+%2B+%283%2F4%29%29%5E2
%2B-sqrt%2817%2F16%29+=+x+%2B+%283%2F4%29
So x+=+-3%2F4+%2B-sqrt%2817%2F16%29, which gives you your two x intercepts. Hope this helps!