How do I graph this function? And how do I find the axis of symmetry, and the maximum or minimum value?

Question

The function is h(x)=-2(x-1)^2-3

I know the answers from the back of the book, but I don't understand how to find them. Also do I need to find the axis of symmetry and min/max value before or after I graph the function? All it says is "For each of the following, graph the function by hand and find the vertex, the axis of symmetry, and the maximum value or the minimum value."

Please explain to me HOW to get the answers. Thanks!!!!!!!!

Also, I don't have a graphing calculator. There's a way to do this by hand, right?

Answer 1

this isa parabola opening downwards
vertices are 1 and 3
a=-2
give x different values say -3,-2,-1,0,1,2,3 and fing the corresponding values of y
tabulate and plot the ordered pairs

Answer 2

The vertex form of a parabola is y = a(x-h)^2 + k where (h,k) is the vertex. So your vertex is (1,3)

The axis of symmetry passes through the vertex and has the same x-value, so yours is x=1

The maximum value is found, since a (the number in front of x^2) is negative. You find it by getting the y-coordinate of the vertex, which is 3. There is no minimum value.

To graph by hand, plot the vertex. Then replace x with x-values near the vertex's x value, like 2, 3, 4; 0, -1, -2, find the corresponding value for h(x) [which becomes y on the graph], and plot these points.

Answer 3

The vertex is at : x = -b/2a = 4/ 2 =2 y = 2^2 - 4*2 +9 = 5 vertex : ( 4 , 5 ) elect the spectacular axis of symmetry(a)y=5(b)x=2(c)x= -2(d)y= -5 answer is (b) x = 2 Does f(x)have a max or min fee? the coefficient of x^2 is effective, so minimum. Max/min fee= 5..........[ the y - cordinate of the vertex is the graph going upward or downward, upward

Answer 4

The vertex is (h,k) where the function is f(x)=a(x-h)^2+k. In your case (1,-3). The axis of symmetry is x=h. In your case, x=1. The maximum point is at (h, f(h)). In your case, (1, h(1)) = (1, -3).
If you need a calculator here is one online for free. http://www.coolmath.com/graphit/index.html

Answer 5

To graph a function by hand, you draw up a table of values. I know it sounds strange and so darned old-fashioned, but that's the way you do it. From your graph, you can get the approximate answers to those questions.

Answer 6

hope this helps...
i think u need 2 differentiate it first
from that u can find the values of x and y
u find the second derivative to see if its a max or min
draw your graph now coz u no were it crosses x and y and u no which way the graph goes when u find max or min

Answer 7

use a graphing calculator! after graphing the function, there should be menus that will find the max and min for you. then copy the function on a piece of graph paper. that's how my calc teacher told my class to do it in high school.