Find the vertex of the parabola
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Find the vertex of the parabola
To solve for the vertex of the parabola given by the equation , we start by comparing the equation with the standard vertex form of a quadratic function: .
In the given equation, , we identify:
- , which corresponds to the horizontal shift of the parabola.
- , which represents the vertical shift.
Therefore, the vertex of the parabola is at the point , which is .
Thus, the vertex of the parabola is .
The following function has been graphed below:
\( f(x)=x^2-6x \)
Calculate point C.
Great question! In vertex form , the pattern is (x - h). When you see (x - 3), it means h = 3, not -3. Think of it as "x minus 3 equals zero when x = 3".
Then you'd rewrite it as , so h = -3 and the vertex would be (-3, -1). The plus sign means h is negative!
Use the pattern (h, k) where h comes from the x-part and k comes from the y-part. In , h affects x-direction and k affects y-direction.
Absolutely! The vertex is the lowest point (if a > 0) or highest point (if a < 0) of the parabola. Since our coefficient of the squared term is 1 (positive), (3, -1) should be the minimum point.
If you see something like , then k = 0! The vertex would be (2, 0). Missing terms just mean their value is zero.
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