Problem 50
Question
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.
Step-by-Step Solution
Verified Answer
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).
1Step 1: 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.
2Step 2: 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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