Question

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

Answer 1

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

Answer 2

so now when you put y =0

0 = -3x^2 + x +4

then you factor out

Answer 3

\[-3x^2 + +4x - 3x +4=0\]

\[-3x(x +1) +4(x +1)=0\]

\[ (x+1) +(-3x +4) = 0 \]

\[x = -1 , \frac{4}{3} \]

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

times means \[\times\]