Question

Write the formula for the parabola that has x-intercepts (−2,0) and (4.6,0), and y-intercept (0,1.5)

Answer 1

To start, what is the generic formula for a parabola?

Answer 2

given the roots,
y = a(x+2.0)(x-4.6)
Now plug in the point (0,1.5) and you get
a(0+2.0)(0-4.6) = 1.5
-9.2a = 1.5
a = -1.5/9.2 ≈ -0.16
That means
y = -0.16(x+2.0)(x-4.6)

You can massage that into whatever form you need.

Answer 3

Y = Ax^2 + Bx + C.
C = -4.6 * 2 = -9.2.
B = -4.6 + 2 = -2.6.

h = (-2 + 4.6)/2 = 1.3.
h = -B/2A = 1.3.
2.6/2A = 1.3,
A = 1.
Eq: Y = x^2 - 2.6x - 9.2.

Answer 4

Note: The given x-int. satisfy my Eq., but my y-int. is -9.2 instead of 1.5.

Answer 5

parabola x intercept form is:
y=a(x-x1)(x-x2)
x1 and x2 being the x intercepts

x intercepts are -2 and 4.6
-(-2)=2
-(4.6)=4.6
therefore
y=a(x+2)(x-4.6)

to solve for a substitute with the other coordinate they give you (0,1.5)
1.5=a(0+2)(0-4.6)
1.5=a*2*-4.6
1.5= -9.2a
1.5/-9.2 = a
-1.5/9.2 = a

answer: 1.5=(-1.5/9.2)(0+2)(0-4.6)

hope this helps :)

Answer 6

in my answer i put 0 instead of x and 1.5 instead of y I am so sorry the answer should be y=(-1.5/9.2)(x+2)(x-4.6) not 1.5=(-1.5/9.2)(0+2)(0-4.6)

y=(-1.5/9.2)(x+2)(x-4.6)

Answer 7

The answer should be:
y=(-1.5/9.2)(x^2 - 2.6 - 9.2)

Answer 8

The correct answer is y=(-1.5/9.2)(x^2 - 2.6 - 9.2)