Reed Elliott
07/22/2024 · Elementary School

Find the \( y \)-intercept(s) and \( x \)-intercept(s) of the graph of the following. \[ y=x^{2}-49 \] If there is more than one answer, separate them with commas. Click on "None" if applicable. \( y \)-intercept(s):

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To find the \( y \)-intercept of the graph of the equation \( y = x^2 - 49 \), we set \( x = 0 \): \[ y = 0^2 - 49 = -49 \] Thus, the \( y \)-intercept is: \[ (0, -49) \] Next, to find the \( x \)-intercepts, we set \( y = 0 \): \[ 0 = x^2 - 49 \] This can be rearranged to: \[ x^2 = 49 \] Taking the square root of both sides gives: \[ x = 7 \quad \text{or} \quad x = -7 \] Thus, the \( x \)-intercepts are: \[ (7, 0), (-7, 0) \] In summary, the intercepts are: - \( y \)-intercept(s): \(-49\) - \( x \)-intercept(s): \(7, -7\) So, the final answers are: **\( y \)-intercept(s):** \(-49\) **\( x \)-intercept(s):** \(7, -7\)

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\( y \)-intercept(s): -49 \( x \)-intercept(s): 7, -7
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