Find the standard equation of a parabola with zeros at x=2 and x=15 passing through the point (6,−5).
thank you
Remember to write your answers as exact numbers (fractions), rather than a decimal approximation.
i need the answer in this form:
y=...(x+-)^2 +-.....
Your equation will have the form
y = a(x-2)(x-15)
but (6,-5) is on it, so that lets us find a
-5 = a(6-2)(6-15)
a = 5/36
y = (5/36)(x^2 - 17x + 30)
= (5/36)(x^2 - 17/2 + 289/4 - 289/4 + 30)
= (5/36)( (x - 17/2)^2 - 289/4 + 30)
= (5/36)(x - 17/2)^2 - 845/144
Sorry,I don't get it
thank you
never mind....I got it oobleck
thank you
passes through:
(2 , 0)
(15 , 0)
(6 , -5 )
y = a x^2 + bx + c
0 = 4 a +2 b + c
0 = 225 a + 15 b + c
-5 = 36 a + 6 b + c
3 equations, 3 unkmowns
221a +13 b = 0 .....so b = -221 a/13
189 a + 9 b= 5
so
189 a + 9 (-221 a/13) = 5
2457 a - 1989 a = 65
468 a = 65
a = 65/468
go back and get b and c
I thought this was already done. The zeroes mean
y = a(x-2)(x-15)
the point means
a(6-2)(6-15) = -5
a = 5/36
y = 5/36 (x-2)(x-15)
In standard form, that is (x-h)^2 = 4p(y-k) we get
(x - 17/2)^2 = 36/5 (y + 845/144)
To find the standard equation of a parabola with zeros at x = 2 and x = 15 passing through the point (6, -5), you need to follow a few steps:
Step 1: Find the equation of the parabola in factored form
Since the zeros are given as x = 2 and x = 15, the factored form of the equation can be written as follows:
y = a(x - 2)(x - 15)
Step 2: Substitute the given point into the equation
Substituting the coordinates of the given point (6, -5) into the equation, we get:
-5 = a(6 - 2)(6 - 15)
Step 3: Solve for "a"
Now, we can solve for "a" by simplifying the equation:
-5 = a(4)(-9)
-5 = -36a
Dividing both sides of the equation by -36, we get:
a = -5 / -36
a = 5 / 36
Step 4: Substitute "a" back into the factored form
Now, substitute the value of "a" back into the factored form of the equation:
y = (5 / 36)(x - 2)(x - 15)
Step 5: Expand the equation
To convert the equation into standard form, we need to expand it:
y = (5 / 36)(x^2 - 17x + 30)
Step 6: Simplify the equation
Finally, simplify the equation by distributing the fraction:
y = (5 / 36)x^2 - (85 / 36)x + (25 / 6)
Therefore, the standard equation of the parabola with zeros at x = 2 and x = 15 passing through the point (6, -5) is:
y = (5 / 36)x^2 - (85 / 36)x + (25 / 6)