## Algebra 2 Common Core

$2\text{$x$-intercepts}$
Using $y=ax^2+bx+c,$ the given equation, \begin{align*} y=-5x^2-4x+3 ,\end{align*} has $a= -5 ,$ $b= -4 ,$ and $c= 3 .$ Using the Discriminant Formula which is given by $b^2-4ac,$ the value of the discriminant is \begin{array}{l}\require{cancel} & (-4)^2-4(-5)(3) \\&= 16+60 \\&= 76 \end{array} Since the discriminant is greater than $0,$ then there are $2$ real solutions. With $2$ real solutions, then the graph of the given equation has $2\text{$x$-intercepts} .$