70 POINTS! PLEASE HELP! Explain the difference between the following equation formats: Slope-Intercept, Point-Slope and Standard
1 answer:
You might be interested in
Answer:
Step-by-step explanation:
The vertex form for a quadratic equation has the following form:
Where the vertice of the equation is the point (h, k)
To transform the equation in its vertex forms we must find its vertex.
Be a quadratic equation of the form:
Where a, b and c are real numbers, then the vertex of the equation will be:
For the given equation:
Therefore the vertice is:
Now we substitute x = 6 into the equation and find the value of k.
Therefore the vertice is: (6, -16)
And the equation is:
Given:
The parent function is
Consider the transformed function is g(x) instead of f(x) because both functions are different.
Step-by-step explanation:
We have,
It can be written as
...(i)
The translation is defined as
.... (ii)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If 0<|k|<1, then the graph compressed vertically by factor k and if |k|>1, then the graph stretch vertically by factor k.
If k is negative, then f(x) is reflected across the x-axis to get g(x).
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
On comparing (i) and (ii), we get
, f(x) shifts 4 units right.
, f(x) shifts 8 units down.
, it is negative so f(x) reflected across the x-axis.
, so f(x) stretched vertically by factor 5.
Therefore, the function f(x) reflected across the x-axis, stretched vertically by factor 5 and shifted 4 units right 8 units down to get g(x).