Quadratic formula and discriminant

roots

x-intercepts

zeros

All of the above

Factoring Method

Completing the Square Method

Quadratic Formula

Square Root Method

a = 2 , b = 3, c = -5

a = 2, b = -3, c = 5

a = 2, b = -3, c = -5

a = -2, b = 3, c = 5

$x=\frac{b-\sqrt{\left(b\right)^2-4\left(a\right)\left(c\right)}}{2\left(a\right)}$

$x=\frac{-\left(b\right)\pm\sqrt{\left(b\right)^2-4\left(a\right)\left(c\right)}}{2\left(a\right)}$

$x=\frac{\left(b\right)\pm\sqrt{\left(b\right)^2-4\left(a\right)\left(c\right)}}{2a}$

$x=-\left(b\right)\pm\sqrt{b\pm4\left(a\right)\left(c\right)}$

The maximum or minimum value

The y-intercept

The number and type of solutions

The axis of symmetry

 $\frac{-b}{2a}$  

 $b^2-4ac$  

 $ax^2+bx+c$  

 $\frac{-b\pm\sqrt{b^2-4ac}}{2a}$  

None

One

Two

Infinite

None

One

Two

Infinite

None

One

Two

Infinite

 $\left(-19\right)^2-4\left(3\right)\left(20\right)$  

 $\left(-19\right)^2-4\left(3\right)\left(-20\right)$  

 $\left(-20\right)^2-4\left(3\right)\left(-19\right)$  

 $-\left(-19\right)^2-4\left(3\right)\left(-20\right)$  

64

52

9

0

Positive

Negative

Zero

76

29

68

none of these

76

-7

9

none of these

Positive

Negative

Zero