Question

An expression is shown below:
f(x)=-16x^2+8x+3

Part A: What are the x intercepts of the graph of the f(x)? Show your work.

Part B: Is the vertex of the graph of f(x) going to be maximum or minimum? What are the coordinates of the vertex? Justify your answer and show your work.

Part C: What are the steps you would use to graph f(x)? Justify that you can use the answer obtained in Part A and Part B to draw the graph.

Answer 1

let y = f(x)

you then have a standard quadratic for y= -16x^2+8x+3

This cannot be factorised, so use quadratic formula for finding y=0 i.e. intercepts on x axis

You can tell if it's a max or min by the sign of the factor of x

you can work out the ordinate of the vertex from x = -b/2a

Tht gives you 3 points and the shape of the curve :