Question

Without drawing the graph of the equation, determine how many points the given equation have in common with the x-axis and where is the vertex in relation to the x-axis?
y = -2x^2 + x + 3

Answer 1

Remark
It's asking you to complete the square to find the vertex. 

Solve
y = -2x^2 + x + 3 Put brackets around the first 2 terms.
y = (-2x^2 + x) + 3    Pull out the 2.
y = -2(x^2 - 1/2 x) + 3 Be especially observant of the sign on 1/2x Divide the middle term's number by 2 and square it. 
y = -2(x^2 - 1/2 x + [(1/2) / 2]^2 ) + 3 [1/2 divided by 2 is 1/4. (1/4)^2 = 1/16; 2*(1/16) = 1/8
y = - 2(x^2 - 1/2 x + (1/4)^2 ) + 3 + 1/8
y = -2(x - 1/4)^2 + 3 1/8

Comment
Answer to your question. The maximum value (3 1/8) is above the y axis. That means the graph of the equation crosses the x axis twice. I'm going to include the graph because in answering the question, there is no harm in seeing the graph.