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# Quadratic equation

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Please explain and show work

Y=2x^2+12x+19

Find

discriminant

nature of solutions

relationship to x axis

solution

vertex

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#### Solution Preview

Y=2x^2+12x+19

discriminant

nature of solutions

relationship to x axis

solution

vertex

please explain and show work
Solution:
Discriminant:
Remember that the solution of the quadratic equation
a x2 + b x + c = 0
is given by the quadratic formula

________________________________________ ________________________________________
-b ± b2 - 4 a c
x = ________________________________________ ________________________________________
2 a
The discriminant of a quadratic equation is simply the expression inside the square root in this formula :
D = b2 - 4 a c
To make the working a bit clearer, we can rewrite the equation
2 x2 + 12 x + 19 = 0
as
2 x2 + 12 x + 19 = 0.
Comparing this with
a x2 + b x + c = 0
shows that
a = 2 , b = 12 and c = 19.
Substituting ...

#### Solution Summary

This shows how to find the discriminant, solution, and vertex for a quadratic equation.

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