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Chapter 1: Problem 30

Find the \(x\) - and \(y\) -intercepts of the graph of the equation. $$y=x^{4}-25$$

Short Answer

Expert verified
The x-intercepts for the equation are at points (5,0) and (-5,0), and the y-intercept is at point (0,-25).

Step by step solution

01

Find the x-intercepts

To find when the graph crosses the x-axis, set \(y = 0\) and solve for \(x\). The equation becomes \(0 = x^{4} - 25\). Solve this equation to find the value of x as follows: \[ x^{4} = 25 \] \[ x = \sqrt[4]{25} \] This gives two solutions for \(x\), which are \(x = \pm5\). This means the graph crosses the x-axis at (5,0) and (-5,0).
02

Find the y-intercept

To find where the graph crosses the y-axis, set \(x = 0\) and solve for \(y\). The equation becomes \( y = (0)^{4} - 25\). Calculating this, y equals -25. Hence, the y-intercept is at point (0,-25).

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