Quadratic Functions

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 is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens.

Front

How do you find the axis of symmetry for a parabola?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the standard form of the quadratic equation.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating the function at x = 0.

Front

What is the formula for the vertex of a parabola given in standard form?

Back

The vertex (h, k) can be found using h = -b/(2a) and k = f(h), where f(x) is the quadratic function.

Front

What does it mean for a parabola to open upwards?

Back

A parabola opens upwards if the coefficient 'a' in the quadratic equation y = ax² + bx + c is positive.

Front

What does it mean for a parabola to open downwards?

Back

A parabola opens downwards if the coefficient 'a' in the quadratic equation y = ax² + bx + c is negative.

Front

How do you convert from factored form to standard form?

Back

To convert from factored form y = a(x - p)(x - q) to standard form, expand the expression to get y = ax² + bx + c.

Front

What is the discriminant of a quadratic equation?

Back

The discriminant is given by the formula D = b² - 4ac and determines the nature of the roots of the quadratic equation.