Finding the Equation of a Parabola

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In summary, to find the equation of a quadratic function with the given points, we can use the method of solving a system of equations or by using the vertex form of a quadratic equation. By finding the vertex, we can determine the constants and create the equation.
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missnerdist
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Find the equation of a quadratic function whose graph contains the given points.
(-2,1), (-6,1), (2,-7)

THANK YOU
 
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  • #2
Find the equation of a quadratic function whose graph contains the given points.
(-2,1), (-6,1), (2,-7)

solve the system for \(\displaystyle y = ax^2+bx+c\) ...

$a(-2)^2 + b(-2) + c = 1$

$a(-6)^2 + b(-6) + c = 1$

$a(2)^2 + b(2) + c = -7$
 
  • #3
One other method ... note the two coordinates with the same y-value.

a parabola's vertical line of symmetry would pass through the midpoint of those two points, i.e. $x=-4$

using the vertex form for a quadratic equation, $y=a(x-h)^2+k$, the vertex is at the coordinates $(h,k)$.

so, you know $h=-4$ and you have three sets of coordinates ... you should be able to substitute those values to determine the constants $a$ and $k$.
 

What is a parabola?

A parabola is a U-shaped curve that is formed by the graph of a quadratic function. It is a type of conic section and is one of the most commonly studied shapes in mathematics.

How do you find the equation of a parabola?

To find the equation of a parabola, you need to know the coordinates of its vertex and at least two other points on the parabola. You can then use the standard form of a quadratic equation, y = ax^2 + bx + c, and plug in the coordinates to solve for the values of a, b, and c.

What is the standard form of a quadratic equation?

The standard form of a quadratic equation is y = ax^2 + bx + c, where a, b, and c are constants. This form is also known as the vertex form, as it is often used to find the coordinates of the vertex of a parabola.

What is the vertex of a parabola?

The vertex of a parabola is the point on the graph where the parabola changes direction from increasing to decreasing, or vice versa. It is the highest or lowest point on the parabola, depending on whether it opens upward or downward.

Can you find the equation of a parabola if you only know one point on the graph?

No, you need to know at least two points on the parabola to find its equation. This is because a parabola can have an infinite number of equations that pass through a single point. However, if you know the coordinates of the vertex and one other point, you can find the equation of the parabola using the method described in the second question.

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