AMA Flashcard 10.-10.3

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the point where the graph changes direction. It is the highest or lowest point of the parabola, depending on its orientation.

Front

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

Back

The vertex can be found using the formula: \( x = -\frac{b}{2a} \). Substitute this x-value back into the equation to find the y-coordinate.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is \( y = ax^2 + bx + c \), where a, b, and c are constants.

Front

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

Back

The 'a' value determines the direction of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the y-intercept of a quadratic function?

Back

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

Front

Back

The solutions are x = 7, 2.

Front

What is the quadratic formula?

Back

The quadratic formula is \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), used to find the roots of a quadratic equation.

Front

How do you determine the number of real solutions for a quadratic equation?

Back

The number of real solutions can be determined by the discriminant, \( D = b^2 - 4ac \). If D > 0, there are two real solutions; if D = 0, there is one real solution; if D < 0, there are no real solutions.

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: \( x = -\frac{b}{2a} \).

Front

What is the significance of the vertex in a real-world context?

Back

The vertex can represent maximum or minimum values in real-world scenarios, such as profit maximization or cost minimization.