Question

The graph of a function of the form f(x)=ax2+bx+c for different values of a, b, and c is given. For the function, find the following.(a) Determine if the discriminant is positive, negative, or zero.(b) Determine if there are 0, 1, or 2 real solutions to f(x)=0.(c) Solve the equation f(x)=0.

Answer 1

The discriminant is positive since there are two solutions of f (x) = 0

Which can be seen in the graph as it has two intersections with the x-axis.

f(x)=0 when x=-4 or x=2, because the points (-4,0) and (2,0) belong to the function.

Then:

a) The discriminant is positive.

b) There are 2 real solutions to f(x)=0

c)The coordinate of a point belonging to the f(x) function is (x, f (x)), and that second part of the point is what we need to be 0, in other words we must find the intersections of the graph with y = 0, the x-axis.

The points (-4,0) and (2,0) belong to the given function and intercept the x-axis, then

x= - 4 and x = 2 are the solutions for f(x)=0