Chapter 11: Q. 11.29 (page 1093)

Graph $x = - y^{2} - 4 y + 12$ by using properties.

Short Answer

Expert verified

The graph for the equation $x = - y^{2} - 4 y + 12$ is,

Step by step solution

Step 1 Given equation is,

$x = - y^{2} - 4 y + 12$ .

Compare the given equation with $x = a y^{2} + b y + c$

Identify the constants $a, b, c$ .

$a = - 1, b = - 4, c = 12$ .

Since $a = - 1$ , the parabola opens leftward.

To find the axis of symmetry, $y = \frac{- b}{2 a}$ .

Substitute the known values in the formula.

$y = \frac{- (- 4)}{2 (- 1)} = - 2$

Step 2 The vertex is on the line y=-2.

Substitute $y = - 2$ in the given equation.

$x = - {(- 2)}^{2} - 4 (- 2) + 12 = - 4 + 8 + 12 = 16$

The vertex is, $(16, - 2)$ .

To find the $y$ -intercepts substitute $x = 0$ in the given equation.

$0 = - y^{2} - 4 y + 12 (y + 6) (y - 2) = 0 y = - 6, 2$

The $y$ - intercepts are, $(0, - 6)$ and $(0, 2)$ .

To Find the $x$ - intercepts, substitute $y = 0$ in the given equation.

$x = 0 - 0 + 12 x = 12$

The $x -$ intercepts are, $(12, 0)$ .

The point $(12, 0)$ is two units above the line of symmetry. The symmetric point two units below the line of symmetry is $(12, - 4)$ .

Step 3 Plot a graph by using the known values.

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Graph $x = - y^{2} - 4 y + 12$ by using properties.

Short Answer

Step by step solution

Step 1 Given equation is,

Step 2 The vertex is on the line y=-2.

Step 3 Plot a graph by using the known values.

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Graphx=-y2-4y+12by using properties.

Short Answer

Step by step solution

Step 1 Given equation is,

Step 2 The vertex is on the line y=-2.

Step 3 Plot a graph by using the known values.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Discrete Mathematics

Pure Maths

Decision Maths

Probability and Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Graph $x = - y^{2} - 4 y + 12$ by using properties.