Definition of a Quadratic Function
Key points
- A quadratic function is a polynomial function with a degree of 2.
- The shape of the graph is called a parabola
Quadratic functions are polynomial functions with a degree of 2. They are often used to describe projectile motion or descriptions of area.
- The greatest exponent on the variable is 2.
- It is described by the equation: f(x)=ax^2+bx+c.
- In quadratic functions, the variable is squared.
- When quadratic functions are graphed, they form a “U” shape
- This is known as a parabola.
- The parabola can face up or down.
- It cannot be sideways because it would fail the vertical line test and not classify as a function.
- This is known as a parabola.
Key features of quadratic functions include the vertex and the intercepts:
- The vertex is the maximum/minimum points of the parabola.
- The x-intercept(s), also known as the root(s) or solution(s) are where the line passes through or touches the x-axis.
- There are one or two x-intercepts for a quadratic graph.
- The y-value is 0: (x,0)
- The y-intercept is where the line meets the y-axis.
- The x-value is 0: (0,y).
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