Quadratic Equations and Their Properties

These flashcards cover key concepts related to quadratic equations, their standard and vertex forms, properties, and examples of vertical motion problems.

What is the standard form of a quadratic equation?

f(x) = ax² + bx + c.

What does it indicate if a > 0 in the standard form of a quadratic equation?

The parabola opens upward.

How does the absolute value of a affect the width of the parabola?

If a > 1, it is narrower; if |a| < 1, it is wider.

What is the y-intercept of a quadratic equation in standard form?

The constant c is the y-intercept of the graph.

How can you find the x-coordinate of the vertex of a quadratic equation in standard form?

Using the formula x = -b/(2a).

What is the vertex form of a quadratic equation?

f(x) = a(x − h)² + k.

What point represents the vertex in vertex form?

The vertex is at the point (h, k).

What is the axis of symmetry in vertex form?

The axis of symmetry is the vertical line x = h.

What formula is used to find the average rate of change of a function?

Average rate of change = y1-y2/x1-x2

What is the standard formula for vertical motion?

h(t) = -16t² + V₀t + h₀.

What determines the direction of the parabola in a quadratic equation?

The leading coefficient 'a'.

How do you calculate the maximum or minimum value of a quadratic function?

Plug the x-value of the vertex back into the original function to find the corresponding y-coordinate.

What does the 'k' value represent in vertex form?

The constant term added or subtracted outside the parentheses.

How do you determine if the value 'k' is a maximum or minimum?

If 'a' is positive (a > 0), 'k' is the minimum; if 'a' is negative (a < 0), 'k' is the maximum.