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Chapter 7: Problem 28

Use the directions for Exercises 9-14 to graph each quadratic function. Use the quadratic formula to find \(x\)-intercepts, rounded to the nearest tenth. \(f(x)=-3 x^{2}+6 x-2\)

Short Answer

Expert verified
The x-intercepts are approximately 0.4 and 1.7, and the vertex is (1,1). We can use these points to sketch the graph of the function.

Step by step solution

01

Find the x-intercepts

To find the x-intercepts, insert the coefficients into the quadratic formula, which is given by \(-b卤\sqrt{b^{2}-4ac}/2a\). Substitute \(a=-3, b=6, c=-2\) into this formula, to obtain the x-intercepts.
02

Calculate the vertex of the quadratic function

The vertex of a quadratic function is given by \(-b/2a\). Plug in the values \(a=-3\) and \(b=6\) into this formula to obtain the x-coordinate of the vertex. Then plug this value into the given quadratic function to obtain the y-coordinate.
03

Sketch the graph

Plot the x-intercepts and the vertex on the coordinate plane. Because the coefficient of \(x^{2}\) is negative, the graph will open downwards. Sketch the graph of the function by drawing a curve that passes through the vertex and the x-intercepts, and that is concave down.

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