can u help me with these math problems?

Question

FInd an equation for the qudratic function described:

Question 1: The minimum value of f is f(f) = -5 and, f(-1) = 2

Question 2: Its graph is a parabola that is tangent to teh x-axis at (4,0) abd has y-intercept 6.

WOULD BE GOOD IF SOMEONE SHOWED ME HOW TO DO THESE 2 PROBLEMS THANKS.

Answer 1

y = x^2 has a vertex (minimum value) at the origin. To move the vertex to the right or left you have to change the formula. Take #2, for instance: the parabola's vertex is at (4, 0), so the formula must change to y = (x - 4)^2 or y = x^2 - 8x + 16. We're not done yet, because the y-intercept is 6. It should be 16, so we know the curve has been flattened by a factor of 3/8. So our final equation: y = (3/8)(x - 4)^2

There is not enough information, I don't think, to come up with an equation for #1.

Answer 2

For question 1:
let y = a(x - h)^2 + k
y is minimum if a > 0 and x - h = 0
if f(f) = -5 is the minimum, then f - h = 0 or h = f and
-5 = a(f - f)^2 + k or k = -5
The equation becomes y = a(x - f)^2 - 5
If f(-1) = 2 then
2 = a(-1 - f)^2 - 5
a = 7 / (f + 1)^2
Therefore, the equation is y = 7(x - f)^2 / (f + 1)^2 - 5
where f cannot be -1

For question 2:
let y = ax^2 + bx + c
If y-intercept is 6 or in other words (0, 6) is a coordinate then
..... 6 = a(0) + b(0) + c
..... c = 6
The equation becomes
..... y = ax^2 + bx + 6
(4, 0) is also a coordinate, then
..... 0 = a(4^2) + b(4) + 6
..... 0 = 16a + 4b + 6
The tangent of y = ax^2 + bx + 6 has the slope
..... y' = 2ax + b (first derivative)
The slope of the x-axis is zero. So
..... 0 = 2a(4) + b
..... 0 = 8a + b
Solving for the two equations:
..... 0 = 16a + 4b + 6
..... 0 = 8a + b
a = 3/8 and b = -3
The equation of the parabola is y = 3x^2 / 8 - 3x + 6

Answer 3

-7= 3x-8 whilst putting -8 to the different component of equation, the sign will exchange, so it relatively is -7+8= 3x which skill a million=3x hence x= a million/3 and don't worry pertaining to to the order, it relatively is no longer proper! there's a rule in math pertaining to to the order! you are able to actual examine it with the aid of substituting a million/3 into the equation i.e -7= 3*a million/3-8 -7=-7!!!

Answer 4

Oi, sorry, would be able to do this IF I hadn't not done math for these 4 months of summer, but I DID study this stuff last year

Answer 5

This might help:
Try going to this math website: http://www.quickmath.com
It has quick solutions to a bunch of different kinds of math problems.
I used it all the time when I was taking algebra.

Answer 6

OF COURSE. I WILL HELP U WHEN I STUDY ALL THESE.