How do you graph # f(x)=3(x-4)^2-5#?

Question

Avery Alexander · Accepted Answer

Refer Explanation section

Given -

#f(x)=3(x-4)^2-5#

It is a quadratic equation in the vertex form.

The vertex form of the quadratic [generally] is -

#y=a(x-h)+k#
Where #(h,k)# is vertex
In our equation -

#h=4# [x coordinate of the vertex]
#k=-5# [y coordinate of the vertex]
Vertex is #(4,-5)#
Take a few values on either side of #x=4#
Calculate corresponding #y# values
Tabulate it.
Graph it.

Abigail Allen · Answer

#y=3x^2-24x+43#
graph{3x^2-24x+43 [-10, 10, -5, 5]}

#y=3(x-4)^2-5# #y=3x^2-24x+48-5# #y=3x^2-24x+43#

Kennedy Adams · Answer

undefined To graph the function f(x) = 3(x - 4)^2 - 5, you can follow these steps:

1. Identify the vertex: The vertex of the parabola is at the point (h, k), where h is the x-coordinate and k is the y-coordinate. In this case, the vertex is (4, -5).

2. Determine the direction of opening: Since the coefficient of the squared term is positive (3), the parabola opens upwards.

3. Find additional points: You can choose additional points on either side of the vertex to plot on the graph. For example, you can pick x-values such as 3, 5, 6, etc., and plug them into the equation to find the corresponding y-values.

4. Plot the points: Use the coordinates of the vertex and the additional points to plot on the coordinate plane.

5. Draw the parabola: Connect the plotted points smoothly to form the graph of the parabola.

Following these steps will help you graph the function f(x) = 3(x - 4)^2 - 5 accurately.