How to find the y-intercept from vertex form?
Understand the Problem
The question is asking for the method to find the y-intercept of a quadratic function given in vertex form. To find the y-intercept, we typically set x = 0 in the equation and solve for y.
Answer
The y-intercept is given by the formula $y = a(h^2) + k$.
Answer for screen readers
The y-intercept is given by the formula:
$$ y = a(h^2) + k $$
Steps to Solve
- Identify the vertex form of the quadratic function
The vertex form of a quadratic function is given as:
$$ y = a(x - h)^2 + k $$
where $(h, k)$ is the vertex of the parabola.
- Set x to 0
To find the y-intercept, substitute $x = 0$ into the vertex form equation.
- Substitute and simplify
Substituting $x = 0$, we get:
$$ y = a(0 - h)^2 + k $$
This simplifies to:
$$ y = a(h^2) + k $$
- Calculate the y-intercept
The result from the previous step gives us the y-intercept, which can be expressed as $y$ when $x = 0$.
The y-intercept is given by the formula:
$$ y = a(h^2) + k $$
More Information
The y-intercept of a quadratic function represents the point where the graph crosses the y-axis. It is especially useful for understanding the behavior of the function, especially when graphing. In vertex form, knowing the vertex and how the coefficient $a$ affects the shape of the parabola is key for analyzing the function.
Tips
- Forgetting to set $x$ to 0 before solving for $y$.
- Misinterpreting the vertex coordinates. The correct substitution must be made from the vertex form.
