MATH SOLVE

3 months ago

Q:
# Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = -8 + x^2 + 7 ?

Accepted Solution

A:

Answer:The function translated 4 units right and 9 units downThe third answerStep-by-step explanation:* To solve the problem you must know how to find the vertex of the quadratic function- In the quadratic function f(x) = ax² + bx + c, the vertex will be (h , k)- h = -b/2a and k = f(-b/2a)* in our problem ∵ f(x) = x²∴ a = 1 , b = 0 , c = 0∵ h = -b/2a∴ h = 0/2(1) = 0∵ k = f(h)∴ k = f(0) = (0)² = 0* The vertex of f(x) is (0 , 0)∵ g(x) = -8x + x² + 7 ⇒ arrange the terms∴ g(x) = x² - 8x + 7∵ a = 1 , b = -8 , c = 7∴ h = -(-8)/2(1) = 8/2 = 4∵ k = g(h)∴ k = g(4) = (4²) - 8(4) + 7 = 16 - 32 + 7 = -9∴ The vertex of g(x) = (4 , -9)* the x-coordinate moves from 0 to 4∴ The function translated 4 units to the right* The y-coordinate moves from 0 to -9∴ The function translated 9 units down* The function translated 4 units right and 9 units down