# Determine the D and R, sketch the graph (2 other points + the axis of symmetry). From the graph, find the approximate zeros of the function. y = 3/4 x^2 - 1/2 x-2Show the complete solution to...

Determine the D and R, sketch the graph (2 other points + the axis of symmetry). From the graph, find the approximate zeros of the function.

y = 3/4 x^2 - 1/2 x-2

Show the complete solution to explain the answer.

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A quadratic equation written in standard form is y = ax^2 + bx + c.

For this equation...

a = 3/4

b = -1/2

c = -2

First, find the axis of symetry. The formula is...

x = -b / 2a

x = (1/2) / (2 * (3/4))

x = 1/3

Sketch the vertical line x = 1/3.

Next find the vertex by substuting 1/3 in for x in the original equation.

y = (3/4)(1/3)^2 - (1/2)(1/3) - 2

y = -25/12 `~~` -2.083

Plot the approximate location of the vertex (1/3, -2).

Finally, substitute two values in for x.

y = (3/4)(1)^2 - (1/2)(1) - 2

y = -1.75

y = (3/4)(-1)^2 - (1/2)(-1) - 2

y = -0.75

Additional points are (1, -1.75) and (-1, -0.75).

Using these points, the vertex, and the line of symmetry, you are able to sketch the parabola.

Here is what the graph should look like: