For the function y = x2 - 4x - 5, perform the following tasks?

Question

Put the function in the form y = a(x - h)2 + k.
What is the line of symmetry
Graph the function using the equation in part a. Explain why it is not necessary to plot points to graph when using y = a (x – h)2 + k.
In your own words, describe how this graph compares to the graph of y = x2?

Answer 1

y = x² - 4x - 5
y = x² - 4x + 4 - 9
y = (x - 2)² - 9

The line of symmetry is the same as the axis.
The axis of
y = a(x - h)² + k is
x = h

The line of symmetry of y = (x - 2)² - 9 is
x = 2

It is not necessary to plot points to graph y = a(x - h)² + k because all you need is the vertex, (h,k) and the direction it opens.
If a > 0, then it opens upward
If a < 0 then it opens downward

The graph is just like y = x² translated to the right h units and translated upward k units (These are my own words!)

^_^

Answer 2

To put the function is standard form, you need to complete the square. If you add 9 to each side, the equation becomes y+9=x^2-4x+4. Then it can be factored into y+9=(x-2)^2. Solving for y gives y = (x-2)^2 - 9. The line of symmetry is the vertical line that passes through the vertex of the parabola. In this case, the vertex is at the point (h,k) = (2, -9). Since this is a vertical line, the equation for the axis of symmetry is x = 2. It's not necessary to plot points because you know that the vertex is at (2, -9) and that the parabola points upward since a is positive. In addition, since a = 1, you know the shape of the parabola. The graph is exactly the same shape as the graph of y = x^2, it has just been shifted over two units to the right and nine units down. Hope all that makes sense...

Answer 3

2) For the function y = x^2 - 4x - 5, carry out right here projects: a) positioned the function contained in the kind y = a(x - h)^2 + ok. answer: y=x^2-4x-5 =x^2-4x+4-4-5 =x^2-4x+4-9 =(x-2)^2-9 b) what's the equation for the line of symmetry for the graph of this function? answer: x=2 c) Graph the function utilizing the equation in part a. clarify why it isn't needed to devise factors to graph even as utilizing y = a (x – h)2 + ok. teach graph right here. rationalization of graphing. d) on your man or woman words, describe how this graph compares to the graph of y = x2? same structure moved contained in the airplane. .

Answer 4

x2 - 4x - 5 = (x2 - 4x +4) -4 - 5
=(x-2)^2-9

(a=1, h=2, k = -9)

line of symmetry is x=2
the graph is regular parabola (y=x^2), shift by 2 to the right, and by 9 down. Since we have a=1, the parabola is not stretched or compressed vertically

Answer 5

y = x^2 - 4x - 5
y = (x^2 -4x) - 5
Divide the coefficient of the x term by two and then square it. Add it inside the parentheses and subtract it outside the parentheses.
y = (x^2 - 4x + 4) - 5 - 4
y = (x-2)^2 - 9
The vertex is (2,-9)
The line of symmetry is x = 2
It is the graph of y = x^2 moved to the right by 2 and down by 9.