How to find the y-intercept of a parabola?
Understand the Problem
The question is asking for the method to find the y-intercept of a parabola, which typically involves evaluating the parabola's equation at x = 0.
Answer
The y-intercept is $c$ in the equation $y = ax^2 + bx + c$.
Answer for screen readers
The y-intercept of the parabola is the constant $c$ in its equation $y = ax^2 + bx + c$.
Steps to Solve
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Identify the equation of the parabola Make sure you have the equation of the parabola in the standard form, which is usually written as $y = ax^2 + bx + c$.
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Substitute x = 0 To find the y-intercept, we need to evaluate the equation when $x = 0$. This means we will substitute 0 in place of $x$ in the equation.
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Solve for y After substituting $x = 0$, the equation simplifies to $y = a(0)^2 + b(0) + c$. This simplifies further to $y = c$. Thus, the y-intercept is simply the value of $c$.
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Conclusion The y-intercept of the parabola is the constant term $c$ in the equation, indicating where the parabola crosses the y-axis.
The y-intercept of the parabola is the constant $c$ in its equation $y = ax^2 + bx + c$.
More Information
The y-intercept is a crucial point on the graph as it represents the value of $y$ when the graph intersects the y-axis, which is useful for graphing and understanding the behavior of the parabola.
Tips
- Confusing $c$ with $b$: Remember that $c$ is the constant term, while $b$ is the coefficient of the linear term $bx$.
- Not simplifying properly when substituting $x = 0$.
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