Quadratic applications

The vertex is the highest or lowest point of the parabola, represented as (h, k) in the vertex form of a quadratic equation y = a(x - h)² + k.

Use the formula x = -b/(2a) where a and b are coefficients from the standard form of the quadratic equation ax² + bx + c.

Setting a quadratic equation to zero allows you to find the x-intercepts (roots) of the function, which are the points where the graph intersects the x-axis.

The maximum height represents the peak point of the projectile's trajectory, which can be found at the vertex of the quadratic function modeling the height.

Set the height equation equal to zero and solve for the time variable.

The height h(t) can be modeled by the equation h(t) = -16t² + vt + h₀, where v is the initial velocity and h₀ is the initial height.

The coefficient indicates the direction of the parabola: if positive, it opens upwards; if negative, it opens downwards.

Use the formula t = -b/(2a) from the standard form of the quadratic equation.

The vertex gives the maximum value if the parabola opens downwards and the minimum value if it opens upwards.

The y-coordinate of the vertex represents the maximum or minimum value of the quantity being modeled, such as height or profit.