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How do you find the vertex given an equation?

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How do you find the vertex given an equation?

Solution

  1. Get the equation in the form y = ax2 + bx + c.
  2. Calculate -b / 2a. This is the x-coordinate of the vertex.
  3. To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y. This is the y-coordinate of the vertex.

How do you find the vertex given two points?

To find the vertex of a parabola, you first need to find x (or y, if your parabola is sideways) through the formula for the axis of symmetry. Then, you’ll use that value to solve for y (or x if your parabola opens to the side) by using the quadratic equation. Those two coordinates are your parabola’s vertex.

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Is the X intercept and vertex the same?

If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value. The x -intercepts are the points at which the parabola crosses the x -axis.

How do you find the vertex focus and directrix of x2-2x + 8Y + 9?

How do you find the vertex, focus and directrix of x2 − 2x + 8y + 9 = 0? or in vertex form as y = a(x −h)2 + k where (h,k) is the vertex and 1 2a is the distance between the vertex and the focus as well the distance between the vertex and the directrix.

How to solve for X2 8×2 8?

Complete the square for x 2 8 x 2 8. Tap for more steps… Consider the vertex form of a parabola. Substitute the values of a a and b b into the formula d = b 2 a d = b 2 a. Simplify the right side. Tap for more steps…

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How do you find the vertex form of 64 64?

Raise 8 8 to the power of 2 2. Multiply 4 4 by 2 2. Divide 64 64 by 8 8. Multiply – 1 − 1 by 8 8. Subtract 8 8 from 0 0. Substitute the values of a a, d d, and e e into the vertex form a ( x + d) 2 + e a ( x + d) 2 + e.

How do you find the vertex of a parabola?

Use the vertex form, y = a ( x − h) 2 + k y = a ( x – h) 2 + k, to determine the values of a a, h h, and k k. Since the value of a a is positive, the parabola opens up. Find the vertex ( h, k) ( h, k). Find p p, the distance from the vertex to the focus. Tap for more steps…