Chapter 9: Q. 9.100 (page 940)

Graph $f (x) = - 3 x^{2} - 6 x + 5$ by using its properties.

Short Answer

Expert verified

The graph of the function is

Step by step solution

Step 1. Given information

Function is $f (x) = - 3 x^{2} - 6 x + 5$ .

We have to plot the graph of the function by using its properties.

Step 2. Find the vertex of parabola.

The vertex of a parabola $f (x) = a x^{2} + b x + c$ is given as $(- \frac{b}{2 a}, f (- \frac{b}{2 a}))$ .

Compare the given function with this equation of parabola.

role="math" localid="1645118371720" $a = - 3 b = - 6 c = 5 - \frac{b}{2 a} = - \frac{- 6}{2 (- 3)} = - 1 f (- \frac{b}{2 a}) = f (- 1) = - 3 {(- 1)}^{2} - 6 (- 1) + 5 = - 3 + 6 + 5 = 8$

Therefore, the vertex is $(- 1, 8)$ .

Step 3. Find the axis of symmetry

The axis of symmetry is $x = - \frac{b}{2 a}$ .

Therefore, the axis of symmetry for the given function will be:

$x = - 1$

Step 4. Find some more points.

Insert the ordered pairs which are satisfying the function $f (x) = - 3 x^{2} - 6 x + 5$ .

x	f(x)	(x,f(x))
-2	1.25	(-2,1.25)
-2.5	5	(-2.5,5)
-1	5	(-1,5)
0.5	1.25	(0.5,1.25)

Step 5. Draw the graph

We get the graph as:

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Graph $f (x) = - 3 x^{2} - 6 x + 5$ by using its properties.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the vertex of parabola.

Step 3. Find the axis of symmetry

Step 4. Find some more points.

Step 5. Draw the graph

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Graphf(x)=−3x2−6x+5by using its properties.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the vertex of parabola.

Step 3. Find the axis of symmetry

Step 4. Find some more points.

Step 5. Draw the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Theoretical and Mathematical Physics

Calculus

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Graph $f (x) = - 3 x^{2} - 6 x + 5$ by using its properties.