Question

How many times does the graph of the function below intersect or touch the x axis? y=-3x^2+x+4​

Answer 1

Answer: Two times.

Step-by-step explanation:

The graph touches the x-axis when the value of "y" is zero.

Then, substitute $y=0$ into the function:

$0=-3x^2+x+4$

Use the Quadratic formula to solve for "x":

$x=\frac{-b\±\sqrt{b^2-4ac}}{2a}$

You can identify that:

$a=-3\\b=1\\c=4$

Then, you can substitute values into the Quadratic formula $x=\frac{-b\±\sqrt{b^2-4ac}}{2a}$, so you get:

$x=\frac{-1\±\sqrt{1^2-4(-3)(4)}}{2(-3)}\\\\x_1=\frac{4}{3}\\\\x_2=-1$

Therefore, the graph of this function touches the x-axis two times.