Solving Example 2D Math

Quadratic Equation Setting a quadratic function = 0, changes it to a quadratic equation ax2 + bx + c = 0 This allows us to solve it for the x-intercepts (roots, zeroes or solutions). We could set the function equal to other values to find when the parabola reaches those values.

Answer the following by a) graphing and b) factoring Ex 1 A model rocket follows the following function: h(t) = -5t2 + 15t + 20 Answer the following by a) graphing and b) factoring Solve the function for h(t) = 0 and Check. What do the roots represent? Do they both make sense? Determine the equation of the axis of symmetry. Determine the coordinates of the vertex. What does the vertex represent? Determine the y-intercept - what does this represent? State the domain and range.

Answers Zeroes at t = -1, t = 4 or at (-1, 0) and (4, 0) When rocket hits the ground. t can’t equal -1s though. The rocket must have launched above the ground. Eqn of AOS is x = 1.5 Vertex at (1.5, 31.25) It represents the maximum height of 31.25 m occurs at 1.5 s The y-intercept is (0, 20) which is the starting height at t = 0s which is at 20 m. D = {t|0≤t ≤4, t Ɛ R} and R = {h(t)|0 ≤ h(t) ≤ 31.25, h(t) Ɛ R}