Quadratics Functions Attributes

Front

What is a quadratic function?

Back

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

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the function crosses the x-axis, found by solving the equation ax² + bx + c = 0.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, located at the point (h, k) in the vertex form y = a(x - h)² + k.

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 equation x = -b/(2a).

Front

What does the 'a' value in a quadratic function indicate?

Back

The 'a' value determines the direction of the parabola's opening: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

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

Back

The y-intercept is found by evaluating the function at x = 0, which gives the point (0, c) in the standard form y = ax² + bx + c.

Front

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

Back

The discriminant (D = b² - 4ac) determines the nature of the roots: D > 0 means two real solutions, D = 0 means one real solution, and D < 0 means no real solutions.

Front

What transformations occur in the function y = (x - 2)² + 4?

Back

This function represents a shift of the parent function y = x², moving it right 2 units and up 4 units.

Front

How can you determine the number of solutions from a quadratic graph?

Back

The number of solutions corresponds to the number of x-intercepts: zero intercepts means no solutions, one intercept means one solution, and two intercepts mean two solutions.

Front

What is the standard form of a quadratic function?

Back

The standard form is y = ax² + bx + c, where a, b, and c are constants.