11.12 Characteristics of Quadratics

Front

What is the highest point of a quadratic graph called?

Back

The highest point of a graph is called the maximum.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph crosses the x-axis, which can be found by solving the equation for x.

Front

How do you find the x-intercepts of the quadratic equation y = ax^2 + bx + c?

Back

Set y to 0 and solve the equation ax^2 + bx + c = 0 for x.

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

What are the solutions to quadratic equations known as?

Back

The solutions to quadratic equations are known as roots or zeros.

Front

What is the vertex of a quadratic function?

Back

The vertex is the point where the parabola changes direction, and it can be found using the formula (-b/(2a), f(-b/(2a))).

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c.

Front

What does the 'a' value in a quadratic equation determine?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola.

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

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

Back

If the coefficient 'a' in the quadratic equation y = ax^2 + bx + c is positive, the parabola opens upwards; if negative, it opens downwards.