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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Step-by-step Solution
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):** \(7, -7\)
Quick Answer
\( y \)-intercept(s): -49
\( x \)-intercept(s): 7, -7
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