When the function is given in vertex form $y=a(x-h)^2+k$, how is the vertex found?
A. $(k, h)$
B. $(x, y)$
C. $(h, k)$
D. $(y, x)$
Answer (2)
The vertex of the quadratic function given in vertex form y = a ( x − h ) 2 + k is found at the coordinates ( h , k ) . Therefore, the correct answer is option C: ( h , k ) .
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The vertex form of a quadratic function is y = a ( x − h ) 2 + k .
The vertex of the parabola in this form is ( h , k ) .
Therefore, the correct answer is (h, k).
The final answer is ( h , k ) .
Explanation
Understanding Vertex Form The vertex form of a quadratic function is given by y = a ( x − h ) 2 + k , where ( h , k ) represents the vertex of the parabola. The question asks us to identify the vertex given the equation in this form.
Identifying the Vertex Comparing the given options with the general form ( h , k ) , we can see that the correct coordinates of the vertex are represented by option c.
Examples
Understanding the vertex form of a quadratic equation is incredibly useful in various real-world applications. For example, engineers use parabolas to design arches in bridges, ensuring stability and optimal load distribution. The vertex represents the highest or lowest point of the arch, which is crucial for structural integrity. Similarly, in physics, the trajectory of a projectile (like a ball thrown in the air) follows a parabolic path, and the vertex indicates the maximum height the projectile reaches. Knowing the vertex allows us to predict and control these phenomena effectively. For instance, if we have a quadratic equation y = 2 ( x − 3 ) 2 + 5 , the vertex is at ( 3 , 5 ) .
