Equation of a Parabola Passing Through (2,-2√2) Opening to the Right

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In summary, the equation of a parabola passing through the point (2,-2√2) and opening to the right is y^2 = 4x. This can be found by using the equation y^2 = 4cx and substituting in the given point to solve for c. The mistake in the student's attempt was only squaring the square root of 2, instead of squaring the entire negative value.
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Homework Statement


Write the equation of a parabola passing through the point (2,-2√2) and opening to the right.


Homework Equations


Parabola with a horizontal axis and vertex (0,0) y^2 = 4cx



The Attempt at a Solution



Since the parabola opens right I will use the equation y^2 = 4cx
I will let x = 2 and y = -2√2
y^2 = 4c(2)
(-2√2)^2 = 4c(2)
2 = 4c(2)
2 = 8c
1/4 = c
y^2 = 4(1/4)x
y^2 = x

* The answer in my student solution mannual says the correct answer should be y^2 = 4x. When I graph this, my graphs supports this answer, where did I go wrong?
 
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  • #2
Sorry, I figured it out. When i squared my y value, i only squared the √2, giving me 2, instead of squaring -2√2 which would give 8.
 

FAQ: Equation of a Parabola Passing Through (2,-2√2) Opening to the Right

What is the equation of a parabola passing through the point (2,-2√2) and opening to the right?

The equation of a parabola passing through the point (2,-2√2) and opening to the right can be written in the form y = a(x-h)^2 + k. The values of h and k represent the coordinates of the vertex, which in this case is (2,-2√2). The value of a determines the shape of the parabola and can be found by plugging in the given point into the equation and solving for a.

How do you find the vertex of a parabola given its equation?

To find the vertex of a parabola given its equation, you can use the formula h = -b/2a, where a and b are the coefficients of the quadratic term and linear term in the equation, respectively. Once you have the value of h, you can find the value of k by plugging h back into the equation and solving for k.

Can a parabola open to the right?

Yes, a parabola can open to the right. The general equation for a parabola is y = ax^2 + bx + c, where a determines the direction in which the parabola opens. If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward. However, if a is zero, the parabola becomes a straight line and does not open in any direction.

How do you graph a parabola opening to the right?

To graph a parabola opening to the right, you can follow these steps:

  1. Find the vertex of the parabola using the formula h = -b/2a.
  2. Plot the vertex on the coordinate plane.
  3. Choose two other points on either side of the vertex and plug them into the equation to find their corresponding y-values.
  4. Plot these points on the graph.
  5. Draw a smooth curve through the points to complete the parabola.

What is the focus of a parabola?

The focus of a parabola is a fixed point on the interior of the parabola that is equidistant from the directrix and the vertex. The coordinates of the focus can be found using the formula (h + 1/4a, k), where h and k are the coordinates of the vertex and a is the coefficient of the quadratic term in the equation. In the case of a parabola opening to the right, the focus will have a y-coordinate equal to the y-coordinate of the vertex.

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