How to find the y-intercept from vertex form?
Understand the Problem
The question is asking how to determine the y-intercept of a parabola when it is expressed in vertex form. In vertex form, a quadratic equation is typically written as y = a(x-h)² + k, where (h, k) is the vertex. To find the y-intercept, we need to evaluate the equation at x = 0.
Answer
The y-intercept is given by $y = a(h^2) + k$.
Answer for screen readers
The y-intercept of the parabola in vertex form is given by $y = a(h^2) + k$.
Steps to Solve
- Substituting x = 0 into the equation
To find the y-intercept, substitute $x = 0$ into the vertex form equation $y = a(x-h)^2 + k$.
- Perform the calculation
The expression becomes: $$y = a(0-h)^2 + k$$
This simplifies to: $$y = a(h^2) + k$$
- Interpret the result
The value of $y$ obtained from the calculation is the y-intercept of the parabola.
The y-intercept of the parabola in vertex form is given by $y = a(h^2) + k$.
More Information
This equation allows us to determine the y-intercept by using the values of $a$, $h$, and $k$ from the vertex form formula. The y-intercept is the point where the curve crosses the y-axis, which helps in graphing the parabola.
Tips
- Confusing the vertex form with standard form. Ensure you correctly use the vertex form $y = a(x-h)^2 + k$ for this calculation.
- Neglecting the square of $(h)$ when substituting into the formula. Remember to compute $(0-h)^2$ carefully.
