Find the vertex of the parabola
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Find the vertex of the parabola
To solve this problem, let's identify the vertex of the given parabola in the form .
The parabola is already given in the vertex form of , which is a special case of the quadratic equation where the vertex () can be read directly from the equation.
Therefore, the vertex of the quadratic function is .
The correct choice from the multiple-choice options provided is the one that matches .
The solution to the problem is the vertex .
Find the standard representation of the following function:
\( f(x)=(x-3)^2+x \)
In vertex form , we have (x - 3), which means h = 3. The vertex moves opposite to the sign inside the parentheses. So (x - 3) shifts the parabola 3 units to the right, not left!
When there's no number added or subtracted outside the squared term, k = 0 by default. Think of it as . The absence of a constant means the vertex sits right on the x-axis.
Substitute the x-coordinate back into the equation! For vertex (3, 0): . If you get the y-coordinate, you're right! The vertex is where the parabola reaches its minimum or maximum.
Then you'd have , so h = -3 and the vertex would be (-3, 0). Remember: , so the parabola shifts 3 units to the left!
Not for finding the vertex! The vertex location depends only on the h and k values in vertex form. Whether it opens up or down (determined by the coefficient of the squared term) doesn't change where the vertex is located.
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