Find the slope of the line graph below?
2 answers:
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The attached picture is a summary of all the six transformations you'd do.
Any change outside the f(x) notation impacts y-values of points on the graph.
Any changes inside the f(x) notation impacts x-values of points on the graph.
The trick is that the inside changes are usually the opposite of what you'd expect to have happen.
7. y=f(x)+8
This is an outside change. You're adding 8 to all the y-values of points on the graph. This will shift your entire graph up 8 units.
8. y=f(x+6)
This is an inside change. Because it says "+6", you want to think, "Ah! That means I'll actually subtract 6 from the x-value of every point on the graph." This graph is shifted 6 units to the left.
9. y=-f(x)
Inside change, impacts y-values. Every y-value will be given the opposite signs. Negatives become positive and positives become negative. This will flip your graph over the x-axis.
10. y = f(-x) + 5
Give this one a shot on your own first in a comment and I'll let you know how you did.
11. y = - 3 f(x-3)
There are three things happening. A negative on the outside, multiplying by 3 on the outside, and subtracting 3 inside. What will each of those do individually? Take a shot on this one and let me know what you think.
12. y = 1/2 f( 1/2 x )
Again, three changes. Try this one and let me know what you think. Remember multiplying by 1/2 inside really means you'll do the opposite of multiplying by 1/2.
Answer:
(5, - 9)
Step-by-step explanation:
Given
f(x) = (x - 8)(x - 2) ← in factored form
Find the zeros by equating f(x) to zero, that is
(x - 8)(x - 2) = 0
Equate each factor to zero and solve for x
x - 8 = 0 ⇒ x = 8
x - 2 = 0 ⇒ x = 2
The vertex lies on the axis of symmetry which is located at the midpoint of the zeros, hence
=
= 5
Substitute x = 5 into f(x) for corresponding y- coordinate
f(5) = (5 - 8)(5 - 2) = (- 3)(3) = - 9
vertex = (5, - 9)