Quadratic Functions

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What do the coefficients 'b' and 'c' represent in the quadratic function?

The coefficient 'b' represents the linear term, which determines the position of the vertex and the direction of the shift. The coefficient 'c' represents the constant term, which determines the y-intercept of the parabola.

What is the general form of the quadratic function?

The general form of a quadratic function is F(x) = ax^2 + bx + c, where a, b, and c are constants.

What does the coefficient 'a' determine in the quadratic function?

The coefficient 'a' determines the shape and direction of the parabola. If a > 0, the parabola opens upwards, and if a < 0, the parabola opens downwards.

What is the vertex form of the quadratic function?

The vertex form of the quadratic function is $f(x) = a(x-h)^2 + k$, where (h, k) represents the coordinates of the vertex.

What is the discriminant of a quadratic function?

The discriminant of a quadratic function $ax^2 + bx + c$ is given by the formula $b^2 - 4ac$.

How many solutions does a quadratic function have when the discriminant is equal to zero?

When the discriminant of a quadratic function is equal to zero, it has one real solution.

Study Notes

Quadratic Function Coefficients

  • In the quadratic function, 'b' represents the coefficient of the linear term, and 'c' represents the constant term.
  • The coefficient 'a' determines the shape of the parabola, with positive 'a' opening upwards and negative 'a' opening downwards.

Quadratic Function Forms

  • The general form of the quadratic function is ax^2 + bx + c, where 'a', 'b', and 'c' are coefficients.
  • The vertex form of the quadratic function is a(x - h)^2 + k, where 'h' is the x-coordinate of the vertex, and 'k' is the y-coordinate of the vertex.

Quadratic Function Discriminant

  • The discriminant of a quadratic function is b^2 - 4ac, which determines the number of solutions.
  • When the discriminant is equal to zero, the quadratic function has exactly one solution, indicating that the graph touches the x-axis at a single point.

Test your knowledge of quadratic functions with this quiz! Learn about the general form of the quadratic function, as well as what the coefficients 'a', 'b', and 'c' mean in the equation.

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