Pregunta
[3. Find the \( y \)-intercept of the parabola \( y=x^{2}+5 x-2 \). Simplify your answer and write it as a proper fraction, improper fraction, or intege
Ask by Harmon Stanley. in the United States
Feb 20,2025
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The \( y \)-intercept is \(-2\).
Solución
To find the \( y \)-intercept of the parabola given by the equation \( y = x^2 + 5x - 2 \), we need to evaluate the function at \( x = 0 \).
1. Substitute \( x = 0 \) into the equation:
\[
y = (0)^2 + 5(0) - 2
\]
2. Simplify the expression:
\[
y = 0 + 0 - 2 = -2
\]
Thus, the \( y \)-intercept of the parabola is \( -2 \).
The final answer is:
\[
\boxed{-2}
\]
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Simplifique esta solución The Deep Dive
To find the \( y \)-intercept of the parabola \( y = x^2 + 5x - 2 \), you need to evaluate the function at \( x = 0 \). Plugging in \( 0 \) gives you \( y = 0^2 + 5(0) - 2 \), which simplifies to \( y = -2 \). So, the \( y \)-intercept is \( (0, -2) \). Finding the intercepts and vertex can provide insights about the graph's symmetry and placement in the coordinate system. The \( y \)-intercept represents where the parabola crosses the \( y \)-axis, which is crucial for sketching the graph accurately and understanding its behavior in various applications, such as physics or economics, where parabolic equations often model real-world scenarios.
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