Answer:
-(x - 1)^2 + 5
Step-by-step explanation:
f(x) = -(x - 1)^2 + 5
This is a form of an equation that gives you lots of information about the parabola (that's the name of the v-ish/u-ish curve shape on the graph)
y = a(x - h)^2 + k
The number in front of the parentheses tells you if the curve is stretched or smashed and if negative (like these) its flipped down so its opening downward.
The number inside the parenthesis added to or subtracted from the x, will tell you if the graph is translated (shifted or slid over) left or right. This left or right shift is kind of backwards from what you might think. An x - 1 means its shifted RIGHT. An
x + anumber will shift it left. Kind of backwards. But there are math reasons. Just memorize the backwardness of horizontal shifts.
The number added on to the end of the equation will translate (slide/shift) the parabola UP for " + anumber" and DOWN for "- anumber" It goes in the direction you would expect for vertical shifts.
The image in the question has been flipped, so start with a negative. Shifted right one, so (x - 1) and lastly, shifted up 5 so tack on a + 5 at the end.
