Final answer:
To write an equation for a parabola with the vertex at (4, -3) and passing through the point (0, 29), the equation is y = 2(x - 4)² - 3.
Step-by-step explanation:
To write an equation for a parabola with the vertex at (4, -3) and passing through the point (0, 29), we can use the standard form of a parabola equation: y = a(x - h)² + k, where (h, k) is the vertex.
Substituting the given vertex into the equation, we have y = a(x - 4)² - 3. To find the value of 'a', we can substitute the coordinates of the given point (0, 29) into the equation: 29 = a(0 - 4)² - 3.
Simplifying this equation, we get 29 = 16a - 3. Rearranging and solving for 'a', we find a = 32/16 = 2.
Therefore, the equation for the parabola is y = 2(x - 4)² - 3.