Solve x(t) = 1/2(3-t)^2

Evaluate

x (t) = \frac{1}{2} (3 - t)^{2}

Write the quadratic function in standard form

x (t) = \frac{1}{2} t^{2} - 3 t + \frac{9}{2}

Find the t -coordinate of the vertex by substituting a= \frac{1}{2} and b= - 3 into t = - \frac{b}{2 a}

t = - \frac{- 3}{2 \times \frac{1}{2}}

Solve the equation for t

t = 3

Find the y-coordinate of the vertex by evaluating the function for t = 3

x (3) = \frac{1}{2} \times 3^{2} - 3 \times 3 + \frac{9}{2}

Calculate

More Steps

x (3) = 0

Solution

(3, 0)

Function