The parent function f(x)=x^2 is translated 2 units left and 3 units up. Write the quadratic function in vertex form.

Question

The vertex form of a quadratic function is f(x)=a(x-h)^2+k.

Answer 1

f(x)=a(x - h)² + k

 

Much like a linear function, k works like b in the slope-intercept formula. Like where add or subtract b would determine where the line crosses, in the linear, k determines the vertex of the parabola. If you're going to go up 2, then you need to add 2.

 

The h determines the movement horizontally. what you put in h determines if it moves left or right. To adjust this, you need to find the number to make the parentheses equal 0 when x equals -2 (because moving the vertex point to the left means subtraction/negatives):

x - h = 0

-2 - h = 0

-h = 2

h = -2

 

So the function ends up looking like:

f(x)=a(x - (-2))² + 2

Subtracting a negative cancels the signs out to make a positive:

f(x)=a(x + 2)² + 2