An expression is shown below: f(x) = 4x2 − 7x − 15 part a: what are the x-intercepts of the graph of f(x)? show your work. (2 points) part b: is the vertex of the graph of f(x) going to be a maximum or minimum? what are the coordinates of the vertex? justify your answers and show your work. (3 points) part c: what are the steps you would use to graph f(x)? justify that you can use the answers obtained in part a and part b to draw the graph. (5 points)

For problems of this nature, i like to start with the graph. a graphing calculator is very .a) the x-intercepts are.. x = -1.25.. x = 3these are found from the graph. they can also be found from the factorization of f(x)... f(x) = (4x +5)(x -3).. f(x) = 0 = (4x +5)(x -3).. x = -5/4, 3b) the vertex will be a minimum, because the coefficient of x^2 is positive. the minimum is the value of f(x) at the line of symmetry, x= (3-1.25)/2 = 0.875... f(0.875) = -18.0625the vertex coordinates are (0.875, -18.0625).c) i would open my graphing calculator and enter the expression.the vertex and zeros are three points on the curve. certainly you can begin a graph of the function when you know three points. the vertical scale factor is 4, so the parabola will be somewhat narrow.

The length of what is left would be 1 1/2 feet long.