take 1/2 of -5, and square it. Add that to both sides.
y+6.25= x^2 -ax + 6.25 +3
y+3.25= (x-2.5)^2
Now, looking at it, wouldn't it by symmetrical abouut x=2.5?
identify the axis of symmetry, create a suitable table of values y=x^2-5x+3
To determine the axis of symmetry for the equation y = x^2 - ax + 6.25 + 3, we need to rewrite the equation in the standard form: y = a(x-h)^2 + k. In this form, (h, k) represents the coordinates of the vertex, which is also the axis of symmetry.
From the equation y + 3.25 = (x - 2.5)^2, we can see that the vertex is at (2.5, -3.25). Therefore, the axis of symmetry is x = 2.5.
To create a suitable table of values for the equation y = x^2 - 5x + 3, we can choose various x-values and calculate the corresponding y-values.
Let's choose five different x-values: -2, -1, 0, 1, and 2.
1. For x = -2:
y = (-2)^2 - 5(-2) + 3
= 4 + 10 + 3
= 17
2. For x = -1:
y = (-1)^2 - 5(-1) + 3
= 1 + 5 + 3
= 9
3. For x = 0:
y = (0)^2 - 5(0) + 3
= 0 + 0 + 3
= 3
4. For x = 1:
y = (1)^2 - 5(1) + 3
= 1 - 5 + 3
= -1
5. For x = 2:
y = (2)^2 - 5(2) + 3
= 4 - 10 + 3
= -3
Therefore, the table of values is as follows:
x | y
---------------
-2 | 17
-1 | 9
0 | 3
1 | -1
2 | -3
This table represents the values of y for the corresponding x-values in the equation y = x^2 - 5x + 3.