8E Unit 8 Flashcard #1: Lessons 1-7

The general form of a quadratic equation is $$ax^2 + bx + c = 0$$ , where a, b, and c are constants and a ≠ 0.

The vertex of a parabola represents the maximum or minimum point of the quadratic function, depending on the direction of the parabola.

To find the maximum height, determine the y-coordinate of the vertex of the parabola, which can be found using the formula $$h = -\frac{b}{2a}$$ .

The roots of a quadratic equation are the x-values where the graph intersects the x-axis, indicating the values of x for which the function equals zero.

Set the height equation equal to zero and solve for time (t).

The coefficient of $$t^2$$ indicates the acceleration due to gravity; a negative value indicates that the object is falling.

The roots can be found using the quadratic formula: $$x = \frac{-b \text{±} \text{√}(b^2 - 4ac)}{2a}$$ .

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation $$x = -\frac{b}{2a}$$ .

In vertex form $$h(t) = a(t-h)^2 + k$$ , the maximum height is the value of k when a < 0.

Projectile motion refers to the motion of an object that is thrown or projected into the air, subject to the force of gravity.