In order to find the image property of quadratic function y = a [X-H] ², What are the symmetry axis, vertex coordinates and maximum of y = a [X-H] &# 178;? I don't want the property of y = a [X-H] &# 178; + K. thank you

In order to find the image property of quadratic function y = a [X-H] ², What are the symmetry axis, vertex coordinates and maximum of y = a [X-H] &# 178;? I don't want the property of y = a [X-H] &# 178; + K. thank you

The axis of symmetry x = h of y = a [X-H] &,
Vertex coordinates (h, 0)
What's the best value
When a < 0, the maximum value of the function is 0,
When a > 0, the minimum value of the function is 0

If the image of quadratic function y = a (X-H) &# + K passes through points (- 2,0) and (4,0), then the value of H is

If two zeros are - 2,4, then the axis of symmetry H = (- 2 + 4) / 2 = 1

Drawing title: known: ∠ AOB, points m and N. calculate: point P, so that point P is on the bisector of ∠ AOB, and PM = PN. (requirement: use ruler to draw, keep the trace of drawing, and do not write the procedure)

In △ ABC, ab = AC, the height BD on the edge of AC = 10cm, P is any point on the edge of BC. PM ⊥ AB and M. PN ⊥ AC and N, find the value of PM + PN

PM + PN = BD = 10, through B as AC parallel line be, extend NP intersection be to F, then angle ABC = angle CBE, P is a point on angle Abe bisector, so PM = PF, BD / / FC, BF / / DC, so FC = BD = 10

In Cartesian coordinates, O is the origin. The image of inverse scale function y = 12 / X passes through point a (2,6)
If the first-order function image passing through point a intersects with the positive half axis of y-axis at point B,
And ob = AB, find the analytic expression of this first-order function
I can do it myself without looking at the picture
2. The ratio of gross profit to purchase price of a commodity is 35%, and the tax payable is 6% of the total price sold
Note: (in commodity operation, the difference between the selling (selling) price and the buying price is usually called gross profit.)
(1) An analytic function of profit (gross profit minus tax) y and sales x
(2) If the sales of the commodity in January is 54000 yuan, the profit of the commodity should be calculated
Answer the second question! No problem one, I can do it!

1
y = x - 6%x - 1*x/(1+35%)
y=269x/1350
two
X = 54000 hours, y = 10760000 hours

It is known that the image with inverse scale function y = k of X and positive scale function y = 2x passes through point a (a, 2), point B is on the x-axis, and OA = ob, so the coordinates of point B are obtained
k=8

The image with positive scale function y = 2x passes through point a (a, 2)
Then 2A = 2
The solution is a = 1
The image with inverse scale function y = K / X passes through point a (1,2)
Then, 2 = K / 1
The solution is k = 2
If the abscissa of point B is x, then
OA²＝1²＋2²＝5
OB²＝x²
From OA = ob, we get
x²＝5
The solution is x = ± 5
So the coordinates of point B are (√ 5,0) or (- √ 5,0)

Let a straight line pass through the fixed point P (1,2) and intersect with the positive half axis of X and Y axes at points a and B respectively to find the minimum area and perimeter of △ AOB
RT
Why let X / A + Y / a = 1?

Let the equation of line l be x / A + Y / b = 1 (a > 0, b > 0)
Then 1 / A + 2 / b = 1
And 1 = 1 / A + 2 / b ≥ 2 √ 2 / AB, that is 1 ≥ 2 √ 2 / ab
Ab ≥ 8
Smin=1/2 ab≥4
If and only if 1 / a = 2 / b
By solving the equations, a = 2, B = 4
So C = 2 √ 5
Cmin=a+b+c=6+2√5
Look at my serious answer. I hope I can help you-<
An equation can be written like that. Do you know the definite range and find the definite product range
Otherwise, we can also use the conventional method to solve, let x = 0, y = 0, respectively find out the coordinates of the intersection point, and then find the maximum value, but this kind of later formula is very troublesome

When a line passes through points (2,1) and intersects the positive half axis of two coordinate axes, the minimum perimeter of the triangle formed by the line and the coordinate axis is obtained

Let the three vertex coordinates of triangle be o (0,0), a (a, 0), B (0, b), where a > 0, b > 0, and OAB = α, α∈ (0, π / 2), then OA = a = 2 + 1 / Tan α ob = b = 1 + 2tan α AB = 1 / sin α + 2 / cos α perimeter = OA + AB + Bo = 3 + 1 / Tan α + 2tan α + 1 / sin α + 2 / cos α = 1 + (3tan (α / 2) + 1) / (Tan (...)

As shown in the figure, given that point m is a point in the first image line of the image with inverse scale function y = K / x, make a vertical line of X axis through point m, and the perpendicular foot is p, if the triangle OMP
The area of K is 5=

Let m (x, y)
∵ PM ⊥ X axis
∴P(x,0)
And ∵ s △ OMP = 5
∴1/2*x*y=5
∴x*y=10
∴k=xy=10

Let P (x, y) move on the image of function y = 4 -- 2x, then the minimum value of 9 ^ x + 3 ^ y is?

Because the point P (x, y) moves on the image of the function y = 4-2x
So y = 4-2x, that is, 2x + y = 4
So 9 ^ x + 3 ^ y
=3^2x+3^y
≥2√[（3^2x）（3^y）]
=2√[3^(2x+y）]
=2√[3^4]
=2*3^2
=18
If and only if 3 ^ 2x = 3 ^ y, y = 2x
That is to say, if x = 1, y = 2, take the equal sign, and 9 ^ x + 3 ^ y has a minimum value of 18