What is the turning point of the parabola with the equation y = 27(x - 64)^2 + 43?
Understand the Problem
The question asks for the turning point (vertex) of a parabola given in vertex form. The equation is in the form y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola. We need to identify the values of h and k from the given equation y = 27(x - 64)^2 + 43.
Answer
$(64, 43)$
Answer for screen readers
$(64, 43)$
Steps to Solve
- Identify the vertex form of a parabola
The vertex form of a parabola is given by the equation: $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex of the parabola.
- Compare the given equation with the vertex form.
We are given the equation $y = 27(x - 64)^2 + 43$. Comparing this with the general vertex form $y = a(x - h)^2 + k$, we can identify the values of $h$ and $k$.
- Determine the value of h
From the equation, we can see that $h = 64$.
- Determine the value of k
From the equation, we can see that $k = 43$.
- State the coordinates of the vertex
The vertex of the parabola is $(h, k) = (64, 43)$.
$(64, 43)$
More Information
The vertex of a parabola in vertex form $y = a(x - h)^2 + k$ is always at the point $(h, k)$. The value of 'a' determines whether the parabola opens upwards (if $a > 0$) or downwards (if $a < 0$) and how "wide" or "narrow" the parabola is, but it does not affect the location of the vertex.
Tips
A common mistake is to incorrectly identify the sign of $h$. Remember the vertex form is $y = a(x - h)^2 + k$, so if you have $(x - 64)$ in the equation, $h$ is $64$, not $-64$. Also, students sometimes mix up $h$ and $k$, so it's important to remember that $h$ is the x-coordinate and $k$ is the y-coordinate of the vertex.
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