How To Find This Quadratic Function?

Thread starter mymachine
Start date May 10, 2013
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Function Quadratic Quadratic function

In summary, a quadratic function is a type of polynomial function with the form f(x) = ax^2 + bx + c, where a, b, and c are constants. The vertex of a quadratic function can be found using the formula x = -b/2a and the quadratic formula can be used to solve for the roots of a quadratic equation. A quadratic function can have zero, one, or two x-intercepts depending on the value of the discriminant. To graph a quadratic function, you can use the vertex and x-intercepts or plot additional points by substituting different x-values into the function.

May 10, 2013

mymachine

How to find the below quadratic function?

y = 0, x = 0
y = 2, x = 1
y = 2, x = -1

Thank you

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May 10, 2013

mfb

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Insights Author

Guess, or make an ansatz and solve for the parameters (this will give 3 linear equations).

1. What is a quadratic function?

A quadratic function is a type of polynomial function with the form f(x) = ax^2 + bx + c, where a, b, and c are constants. It is a second-degree polynomial because the highest exponent of x is 2.

2. How do I find the vertex of a quadratic function?

The vertex of a quadratic function can be found by using the formula x = -b/2a. This will give you the x-coordinate of the vertex. To find the y-coordinate, substitute the x-coordinate into the original function.

3. What is the quadratic formula?

The quadratic formula is a formula used to solve for the roots of a quadratic equation, which is a mathematical expression with the form ax^2 + bx + c = 0. The formula is x = (-b ± √(b^2 - 4ac)) / 2a.

4. Can a quadratic function have more than one x-intercept?

Yes, a quadratic function can have zero, one, or two x-intercepts, depending on the value of the discriminant (b^2 - 4ac) in the quadratic formula. If the discriminant is positive, there will be two distinct x-intercepts. If it is zero, there will be one x-intercept. And if it is negative, there will be no x-intercepts.

5. How do I graph a quadratic function?

To graph a quadratic function, you can use the vertex and x-intercepts. Plot the vertex and the x-intercepts on a coordinate plane, and then draw the parabola passing through those points. You can also plot additional points by substituting different x-values into the function and finding the corresponding y-values.