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Chapter 1: Problem 49

Write each English sentence as an equation in two variables. Then graph the equation. The \(y\) -value is three decreased by the square of the \(x\) -value.

Short Answer

Expert verified
The English sentence 'The \(y\) -value is three decreased by the square of the \(x\)' can be translated into the equation \(y = x^2 - 3\). The graph of this equation is a parabola opening upwards, with its vertex at (0,-3).

Step by step solution

01

Translate English Sentence to Mathematical Equation

The English sentence 'The \(y\) -value is three decreased by the square of the \(x\)' can be translated into a mathematical equation as \(y = x^2 - 3\).
02

Plotting the Graph

The equation obtained, \(y = x^2 - 3\), needs to be plotted on a graph. The graph of a quadratic function such as this one is a parabola. In this case, the graph is a parabola that is translated 3 units down, which means that the vertex is at (0, -3). The graph opens upward, which tells you it's a positive quadratic. Plot points on both sides of the vertex to obtain as accurate a graph as possible.

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Most popular questions from this chapter

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}+x+y-\frac{1}{2}=0$$

Given an equation in \(x\) and \(y,\) how do you determine if its graph is symmetric with respect to the \(x\) -axis?

Find the area of the donut-shaped region bounded by the graphs of \((x-2)^{2}+(y+3)^{2}=25\) and \((x-2)^{2}+(y+3)^{2}=36\).

How is the standard form of a circle's equation obtained from its general form?

Does \((x-3)^{2}+(y-5)^{2}=-25\) represent the equation of a circle? What sort of set is the graph of this equation?
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