Question

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

Answer 1

The answer is 2 times.

Answer 2

when the graph touches x axis at that point y = 0

So, putting y =0
0 = -3x^2 + x +4
so, if you factoriazte it

−3x^2++4x−3x+4=0

−3x(x+1)+4(x+1)=0

(x+1)+(−3x+4)=0

x=−1,4/3

So, two time at -1 and 4/3 it touches the x-axid