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Chapter 1: Problem 50

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

Short Answer

Expert verified
The equation for the given English sentence is \(y = x^2 + 2\). The graph of this equation is an upward-opening parabola with its vertex at (0, 2).

Step by step solution

01

Translate the English sentence into a mathematical equation

The sentence 'The \(y\) -value is two more than the square of the \(x\) -value.' can be translated into the equation \(y = x^2 + 2\). This is because 'two more than' means we are adding two to the value, and 'the square of the \(x\) -value' means \(x\) is squared.
02

Graph the equation

Now that we have the equation \(y = x^2 + 2\), we can graph it. This is a parabola that opens upwards with its vertex at (0, 2). The X-axis values can be chosen from -10 to 10, and for each value of \(x\), we can calculate the corresponding value of \(y\) using the equation, and plot the points. Then we join all the points to get the graph of the equation.

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