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

Question

anonymous · Answer

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

anonymous · Answer

so now when you put y =0 

0 = -3x^2 + x +4

then you factor out

anonymous · Answer

$$-3x^2 + +4x - 3x +4=0$$

$$-3x(x +1) +4(x +1)=0$$

$$ (x+1)  +(-3x +4) = 0  $$

$$x = -1 , \frac{4}{3} $$

anonymous · Answer

this implies at two position $$when x = -1 {  and} \frac{4}{3}$$

anonymous · Answer

Oh, I see. Thank you! I was just having trouble factoring after I realized that was what I was suppose to do.

anonymous · Answer

oh sorry in my second last reply i wrote $$(x + 1) + (-3x + 4)=0$$ it's a typo
instead it is $$(x +1) \ times (-3x + 4) = 0$$

anonymous · Answer

times means $$\times$$