How to find y intercepts from vertex form?
Understand the Problem
The question is asking for the method to find the y-intercepts of a quadratic function given in vertex form. This involves understanding how to manipulate the vertex form equation to determine the point where the graph intersects the y-axis.
Answer
The y-intercept is \( (0, a(h^2) + k) \).
Answer for screen readers
The y-intercept of the quadratic function in vertex form ( f(x) = a(x-h)^2 + k ) is ( (0, a(h^2) + k) ).
Steps to Solve
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Identify the Vertex Form of a Quadratic Function The vertex form of a quadratic function is given by the equation: $$ f(x) = a(x - h)^2 + k $$ where ((h, k)) is the vertex.
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Substitute (x = 0) to Find the y-intercept To find the y-intercept, substitute (x = 0) into the equation. This will give you the function's value at the y-axis: $$ f(0) = a(0 - h)^2 + k $$
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Simplify the Equation Simplify the equation from the previous step: $$ f(0) = a(h^2) + k $$ This result (f(0)) is the y-intercept.
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Final Result The y-intercept is the point ( (0, f(0)) ).
The y-intercept of the quadratic function in vertex form ( f(x) = a(x-h)^2 + k ) is ( (0, a(h^2) + k) ).
More Information
The y-intercept is the point where the graph of the function crosses the y-axis, which occurs when (x = 0). The calculations lead to determining this specific point based on the vertex coordinates.
Tips
- Incorrectly substituting the values of (h) and (k) may lead to an inaccurate calculation of the y-intercept. Always double-check your values in the vertex form.
- Forgetting to square the ((0 - h)) term, which affects the outcome significantly.
