A.7A Key Features of Quadratics

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. It can be found using the formula x = -b/(2a) for a quadratic in the form ax^2 + bx + c.

Front

How do you find the zeros of a quadratic function?

Back

The zeros (or roots) of a quadratic function can be found by setting the function equal to zero and solving for x, either by factoring, using the quadratic formula, or completing the square.

Front

What is the maximum value of a quadratic function?

Back

The maximum value of a quadratic function occurs at the vertex of the parabola when it opens downwards. It can be found using the vertex formula or by evaluating the function at the vertex coordinates.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens upwards or downwards. It can be found using the formula (-b/(2a), f(-b/(2a))) for a quadratic in the form ax^2 + bx + c.

Front

What does it mean for a quadratic function to have one zero?

Back

A quadratic function has one zero (or root) when its graph touches the x-axis at a single point, known as a double root. This occurs when the discriminant (b^2 - 4ac) is equal to zero.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the significance of the coefficient 'a' in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola (upwards if a > 0, downwards if a < 0) and affects the width of the parabola.

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

You can determine the direction of a quadratic function by looking at the sign of the coefficient 'a'. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What is the discriminant of a quadratic function?

Back

The discriminant is the expression b^2 - 4ac in the quadratic formula. It determines the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.