SOLUTION: Sketch a graph of the quadratic function. f(x) = −2x^2 + 5x − 6 Give the vertex, axis of symmetry, and intercepts. (If an answer does not exist, enter DNE.)

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Sketch a graph of the quadratic function. f(x) = −2x^2 + 5x − 6 Give the vertex, axis of symmetry, and intercepts. (If an answer does not exist, enter DNE.)       Log On


   

Question 1071426: Sketch a graph of the quadratic function.
f(x) = −2x^2 + 5x − 6
Give the vertex, axis of symmetry, and intercepts. (If an answer does not exist, enter DNE.)

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
here's your graph.

$$$

your axis of symmetry is x = 1.25

your vertex is (1.25, -2.875).

your y-intercept is y = -6.

there is no x-intercept.

your equation is:
−2x^2 + 5x − 6

since your equation is in standard quadratic equation form of:
ax^2 + bx + c = 0, you get:

a = -2
b = 5
c = -6

you can solve for the vertex using the formula x = -b/2a.
you will get x = -5/-4 = 1.25
you then solve for y by replacing x in the equation with 1.25 to get:
-2*(1.25)^2 + 5*(1.25) - 6 which is equal to -2.875.
your vertex is (1.25,-2.875).

your axis of symmetry is the vertical line through the vertex.
your axis of symmetry is therefore x = 1.25

you solve for the y-intercept by setting x = 0.
you will get y = -2x^2 + 5x - 6 becomes y = -2*0 + 5*0 - 6 which becomes y = -6.

you would factor the quadratic equation to find the x-intercepts.
you will get complex roots which tells you that there is no x-intercept.
you would use the quadratic formula.
when you do, you will get:
1.25 + 1.1989578808282i
1.25 - 1.1989578808282i
It has Complex Roots !
i used an online quadratic equation solver to get these results.
a picture of the results of the use of that solver are shown below:

$$$

i could have done it manually and would have gotten the same results.
the quadratic formula is:


                   -b plus or minus sqrt(b^2 - 4ac)
            x =    --------------------------------
                               2a


you would replace a with -2, b with 5 and c with -6 and solve.

you would get the same answer that the solver is showing you.

the preliminary results would be x = 5/4 plus or minus sqrt(-23)/4.

negative square root indicates complex root.

you would then take the next step to get x = 5/4 plus or minus sqwt(23)/4 * i.

resolve that and you get what the solver is showing you.,

complex roots means the graph is not crossing the x-axis which means you have no x-intercepts.