Chapter 11: Q. 11.30 (page 1093)

Graph $x = - y^{2} + 2 y - 3$ by using properties.

Short Answer

Expert verified

The graph for the function $x = - y^{2} + 2 y - 3$ is,

Step by step solution

Step 1 Given equations are,

$x = - y^{2} + 2 y - 3$ .

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

Identify the constants $a, b, c$ .

$a = - 1, b = 2, c = - 3$

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.

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

Step 2 The vertex is on the line y=1.

Substitute $y = 1$ in the given equation.

$x = - {(1)}^{2} + 2 (1) - 3 = - 1 + 2 - 3 = - 2$

The vertex is, $(- 2, 1)$ .

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

$0 = - y^{2} + 2 y - 3$

The solution of this quadratic equation are the complex numbers. So, there are no $y$ - intercepts.

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

$x = 0 + 0 - 3 x = - 3$

The $x$ - intercepts are, $(- 3, 0)$ .

The point $(- 3, 0)$ is one unit below the line of symmetry. The line of symmetry one unit above the line of symmetry is, $(- 3, 2)$ .

Step 3 Now plot a graph by using the known values.

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Graph $x = - y^{2} + 2 y - 3$ by using properties.

Short Answer

Step by step solution

Step 1 Given equations are,

Step 2 The vertex is on the line y=1.

Step 3 Now plot a graph by using the known values.

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Graphx=-y2+2y-3by using properties.

Short Answer

Step by step solution

Step 1 Given equations are,

Step 2 The vertex is on the line y=1.

Step 3 Now 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

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Graph $x = - y^{2} + 2 y - 3$ by using properties.