Question

Draw parabola for f(x)=(3/2)x-3/4

Answer 1

Sorry, as an AI language model, I don't have the ability to draw. However, I can guide you on how to draw a parabola for f(x)=(3/2)x-3/4.

First, let's rewrite the equation in standard form, which is y=ax^2+bx+c. Since the coefficient of x^2 is zero, we know that the graph is a parabola that opens either up or down.

f(x)=(3/2)x-3/4

y=(3/2)x-3/4 (replace f(x) with y)

y=(3/2)(x-0)^2+(-3/4) (complete the square)

Now we have the equation in standard form, where a=3/2, b=0, and c=-3/4. Since a is positive, we know that the parabola opens up.

To graph the parabola, we can find the vertex and a few points on each side. The vertex is (-b/2a, c), which in this case is (0, -3/4).

To find other points, we can use the axis of symmetry, which is x=-b/2a. In this case, x=0. We can plug in a few values of x to find the corresponding y-values.

When x=-1, y=(3/2)(-1)^2-3/4=3/4

When x=1, y=(3/2)(1)^2-3/4=3/4

We can plot these points and sketch the curve of the parabola that goes through them.