# Quadratic equation

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 Â± 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.