6 Questions
What is the vertex form of a quadratic function?
y = a(x - h)^2 + k
What does 'h' represent in the vertex form of a quadratic function?
Horizontal shift of the parabola
In the vertex form of a quadratic function, what does 'a' determine?
Direction and width of the parabola
In the standard form of a hyperbola, which variable is squared?
Both x and y
What does the coefficient of the squared term in the standard form of a hyperbola determine?
The orientation of the hyperbola
In the standard form of a hyperbola, what does the difference between the squared terms determine?
The eccentricity of the hyperbola
Study Notes
Quadratic Functions
- The vertex form of a quadratic function is a way to express the function in terms of its vertex (minimum or maximum point).
Vertex Form Variables
- In the vertex form, 'h' represents the x-coordinate of the vertex.
- 'a' determines whether the parabola opens upward (a > 0) or downward (a < 0), and its magnitude affects the steepness of the curve.
Hyperbolas
- In the standard form of a hyperbola, the y variable is squared.
Hyperbola Coefficients
- The coefficient of the squared term in the standard form of a hyperbola determines the shape of the hyperbola.
- The difference between the squared terms determines the center of the hyperbola.
Test your knowledge of quadratic functions by taking this quiz on writing quadratic functions into vertex form. Explore the significance of 'h' and 'a' in the vertex form and enhance your understanding of quadratic equations.
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