Question

describe the graph of y=x^2 in words so that someone in a different room could understand exactly what it looks like explain what would happen to the graph if 5 were added to it

Answer 1

* y = x² is a quadratic function represented graphically by parabola opened upward with minimum vertex (0 , 0) and y-intercept = 0

* The graph will move vertically up 5 units and its vertex will be

(0 , 5)

Explanation:

∵ y = ax² + bx + c is a quadratic function

Represented graphically by parabola, its vertex is (-b/2a , f(-b/2a))

∵ The value of a > 0 then the parabola open upward

∴ Its vertex is minimum

∵ The value of a < 0 then the parabola oped downward

∴ Its vertex is maximum

∵ The coefficient of x² = 1

∴ The parabola open upward

∵ The coefficient of x = 0

∴ Its vertex is (0 , 0) ⇒ x = 0/2(1) = 0 , f(0) = (0)² = 0

∴ The y-intercept = 0

∴ The parabola is oped upward , has minimum vertex (0 , 0)

and passing through the origin

∵ 5 is added to y = x² , that means we add 5 to f(x) ⇒ f(x) + 5

∴ y = x² + 5 ⇒ that means the graph move vertically up 5 units

∴ Its vertex will be (0 , 5)