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Really basic quadratic function problem
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- Thread starter YoungPhysicist
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In summary, the conversation is about the difficulty of creating a quadratic function and the fact that it cannot be a function of x. The speaker also mentions finding an expression for x in terms of y and struggling with shifting the parabola upward. The problem is ultimately solved.
- #2
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It has two different values of y for some values of x. It cannot be a function of x. You can find an expression for f such that x=f(y).
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- #4
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FAQ: Really basic quadratic function problem
What is a quadratic function?
A quadratic function is a mathematical function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants and x is the variable. It is called a "quadratic" function because the highest exponent of x is 2.
How do I graph a quadratic function?
To graph a quadratic function, you can make a table of values by choosing different values for x and plugging them into the equation to find corresponding values for y. Then, plot these points on a coordinate plane and connect them with a smooth curve.
What is the vertex of a quadratic function?
The vertex of a quadratic function is the point where the graph changes direction. It is the highest or lowest point on the graph, depending on whether the parabola opens upwards or downwards. The coordinates of the vertex can be found using the formula x = -b/2a and then plugging this value into the equation to find the corresponding y-value.
What is the discriminant of a quadratic function?
The discriminant of a quadratic function is a value that can be calculated using the formula b^2 - 4ac. It is used to determine the nature of the solutions to the quadratic equation. If the discriminant is positive, there are two real solutions. If it is zero, there is one real solution. And if it is negative, there are no real solutions (only complex solutions).
How can I solve a quadratic function?
To solve a quadratic function, you can use the quadratic formula (x = (-b ± √(b^2 - 4ac)) / 2a) or factoring. Factoring involves finding two numbers that multiply to give you the constant term (c) and also add up to give you the coefficient of the x-term (b). These numbers can then be used to rewrite the quadratic equation in factored form, making it easier to find the solutions.