y = (x-6)²-3
1) Let's write a transformation described as it is, algebraically speaking.
• opening upward, (a >0)
,
• shifted 6 units right, (-6)
,
• and three units down -3
2) Starting from the parent function y=x², then we can write:
y = (x-6)²-3
Notice that the horizontal shift is within the parentheses with a swapped sign. And outside that -3 indicating the vertical shift.
Answer:
Step-by-step explanation:
<h3>to understand this</h3><h3>you need to know about:</h3>
<h3>tips and formulas:</h3>
- the parabola crosses f(x) at (4,0)
- the vertex of the parabola (2,6)
- vertex:(h,k)
- h=-b/2a
- k=f(x)
- vertex form:f(x)=a(x-h)²+k
- standard form:ax²+bx+c
<h3>let's solve:</h3>
the vertex form of the equation is
let's figure out a
since the parabola crosses f(x) at (0,4)
therefore
let's figure out b,c
- we have to substitute the value of a into the vertex form and then simply it to get b and c
therefore
- [tex] \sf \: c = 4[/tex