Graph Quadratics

Front

What is the Axis of symmetry?

Back

The Axis of symmetry is a vertical line that divides a parabola into two mirror-image halves. For the quadratic function in the form y = ax^2 + bx + c, the axis of symmetry can be found using the formula x = -b/(2a).

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 whether it opens upwards or downwards. It can be found using the formula for the x-coordinate: x = -b/(2a), and then substituting this value back into the quadratic equation to find the y-coordinate.

Front

What does it mean if a parabola opens upwards?

Back

If a parabola opens upwards, it means that the coefficient of the x^2 term (a) is positive. This indicates that the vertex is a minimum point.

Front

What does it mean if a parabola opens downwards?

Back

If a parabola opens downwards, it means that the coefficient of the x^2 term (a) is negative. This indicates that the vertex is a maximum point.

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero. They can be found using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation in the form ax^2 + bx + c = 0. It is given by: x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root: b² - 4ac. It determines the nature of the roots: if it's positive, there are two real roots; if it's zero, there is one real root; if it's negative, there are no real roots.

Front

What is a maximum value in a quadratic function?

Back

The maximum value of a quadratic function occurs at the vertex when the parabola opens downwards. It is the highest point on the graph.

Front

What is a minimum value in a quadratic function?

Back

The minimum value of a quadratic function occurs at the vertex when the parabola opens upwards. It is the lowest point on the graph.

Front

How do you find the vertex of the quadratic function y = x^2 - 6x + 11?

Back

To find the vertex, use the formula x = -b/(2a). Here, a = 1 and b = -6, so x = 3. Substitute x back into the equation to find y: y = (3)^2 - 6(3) + 11 = 2. Thus, the vertex is (3, 2).