How to find the y intercept from vertex form?
Understand the Problem
The question is asking how to determine the y-intercept of a quadratic function that is expressed in vertex form. The vertex form of a quadratic function is generally written as y = a(x - h)² + k, where (h, k) is the vertex of the parabola. To find the y-intercept, we need to substitute x = 0 into this equation and solve for y.
Answer
$y = ah^2 + k$
Answer for screen readers
The y-intercept of the quadratic function in vertex form is given by $y = ah^2 + k$.
Steps to Solve
- Substitute x = 0 into the vertex form equation
To find the y-intercept, we set $x = 0$ in the equation $y = a(x - h)² + k$.
- Reformulate the equation
Now, we rewrite the equation replacing $x$ with $0$:
$$ y = a(0 - h)² + k $$
- Calculate (0 - h)²
Next, we simplify the expression inside the parentheses:
$$ y = a(-h)² + k $$ $$ y = a(h²) + k $$
- Final equation for the y-intercept
Now we have the expression for the y-intercept:
$$ y = ah² + k $$
At this point, by substituting the values of $a$, $h$, and $k$, we can find the y-intercept.
The y-intercept of the quadratic function in vertex form is given by $y = ah^2 + k$.
More Information
The y-intercept represents the point where the graph of the function intersects the y-axis, which occurs when $x = 0$. This is a useful point when graphing the quadratic function.
Tips
- Confusing the vertex coordinates $(h, k)$ or miscalculating $(0 - h)^2$ as just $h^2$. Make sure to apply the negative correctly during the calculation.
- Forgetting to substitute the correct values of $a$, $h$, and $k$ into the final expression.
