QUADRATIC ATTRIBUTES

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the point where the graph changes direction, representing the maximum or minimum value of the function.

Front

How do you find the y-intercept of a quadratic function?

Back

The y-intercept of a quadratic function can be found by evaluating the function at x = 0, which gives the point (0, c) in the standard form.

Front

What are x-intercepts?

Back

X-intercepts are the points where the graph of a function crosses the x-axis, found by solving the equation f(x) = 0.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b² - 4ac) determines the nature of the roots of the quadratic equation: if D > 0, there are two distinct real solutions; if D = 0, there is one real solution; if D < 0, there are no real solutions.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

Front

How can you determine the number of solutions for a quadratic equation?

Back

The number of solutions can be determined using the discriminant: if D > 0, there are two solutions; if D = 0, there is one solution; if D < 0, there are no solutions.

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value of a quadratic function occurs at the vertex, and can be found by substituting the x-coordinate of the vertex back into the function.

Front

What does it mean if a quadratic function opens upwards?

Back

If a quadratic function opens upwards, it means the coefficient 'a' is positive, indicating that the vertex is a minimum point.