Draw parabola for f(x)=(3/2)x-3/4
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.
To draw the parabola for the function f(x) = (3/2)x - 3/4, we need to follow these steps:
Step 1: Find the vertex of the parabola.
Step 2: Determine the axis of symmetry.
Step 3: Find two points to plot on each side of the vertex.
Step 4: Sketch the parabola using the vertex and the points.
Let's start with step 1:
Step 1: Finding the vertex.
The general form of a quadratic function is y = ax^2 + bx + c, where "a", "b", and "c" are the coefficients of the quadratic equation. In our case, the equation is y = (3/2)x - 3/4.
To find the vertex, we can use the formula: x = -b/2a.
In our case, a = 3/2 and b = 0, since there's no x^2 term. Substituting the values, we get x = 0 / (2 * (3/2)) = 0.
To find the corresponding y-coordinate of the vertex, we substitute the x-coordinate we found back into the equation:
y = (3/2) * 0 - 3/4 = -3/4.
So, the vertex of the parabola is (0, -3/4).
Step 2: Determining the axis of symmetry.
The axis of symmetry is a vertical line passing through the vertex of the parabola. In our case, the axis of symmetry is x = 0.
Step 3: Finding two points to plot on each side of the vertex.
To find the points, we can choose arbitrary values for x and substitute them into the equation to get the corresponding y-coordinates.
For example, let's choose two values for x, say x = -2 and x = 2.
For x = -2:
y = (3/2) * (-2) - 3/4 = -3 - 3/4 = -15/4.
So, the point (-2, -15/4) lies on the parabola.
For x = 2:
y = (3/2) * 2 - 3/4 = 3 - 3/4 = 9/4.
So, the point (2, 9/4) lies on the parabola.
Step 4: Sketching the parabola.
Now, let's plot the vertex (0, -3/4), along with the two points (-2, -15/4) and (2, 9/4) on a graph. Remember to also plot the axis of symmetry at x = 0.
The resulting parabola will be symmetric about the axis of symmetry and go in the direction determined by the coefficient of x^2 (which is 3/2 in our case).