Final answer:
To find the value of 'a' in the quadratic function with a vertex at (3, 4) and another point at (5, 12), we can use the given information. By plugging in the coordinates of the point and solving the resulting equation, we find that a = 2.
Step-by-step explanation:
To find the value of 'a' in the quadratic function, we can use the information given about the vertex and another point on the graph. Since the vertex is at (3, 4), the equation can be written as y = a(x - 3)^2 + 4. Plugging in the coordinates of the other point (5, 12) gives us 12 = a(5 - 3)^2 + 4. Solving this equation for 'a' will give us the correct value.
Starting with the equation 12 = a(5 - 3)^2 + 4, we simplify the expression inside the parentheses: 12 = a(2)^2 + 4. This becomes 12 = 4a + 4 after squaring 2. Moving the constant term to the other side gives us 8 = 4a. Dividing both sides by 4, we find that a = 2.