Question

Find a parabola with equation y = ax2 + bx + c that has slope 1 at x = 1, slope −11 at x = −1, and passes through the point (1, 4).

Answer #1

Find a parabola with equation y = ax2 + bx + c that
has slope 1 at x = 1, slope −21 at x = −1, and
passes through the point (1, 14)

Find a parabola with equation
y = ax2 + bx + c
that has slope
14
at x = 1, slope
−22
at x = −1, and passes through the point
(1, 10).

Find the equation
y = ax2 + bx + c
of the parabola that passes through the points. To verify your
result, use a graphing utility to plot the points and graph the
parabola.
(−8, 0), (−4, −4), (0, 0)

he equation for a parabola has the form ?=??2+??+?y=ax2+bx+c,
where ?a, ?b, and ?c are constants and ?≠0a≠0. Find an equation for
the parabola that passes through the points (−1,−10)(−1,−10),
(−2,−1)(−2,−1), and (−3,18)(−3,18).

Suppose that you were to try to find a parabola y =
ax2 + bx + c that passes through the
(x, y) pairs (-5,12), (-4,-2), and (-2,5). To
obtain the coefficients a, b, and c you
would try to solve a system of linear equations whose augmented
matrix is which?

Find the a, b, c so that y =
ax2 + bx + c goes through the given points.
a. (1, 3), (2, 5), and (3,
1)
b. (-1, -2), (1, -1), and (3,
10)

1) Write the standard form of the equation of the parabola that
has the indicated vertex and whose graph passes through the given
point.
Vertex: (3, −1); point: (5, 7)
f(x) = __
2) Write the standard form of the equation of the parabola that
has the indicated vertex and whose graph passes through the given
point.
Vertex: (4, 5); point: (0, 1)
f(x) = __
3) Write the standard form of the equation of the parabola that
has the indicated...

find the equation of the parabola with vertical axis that passes
through the point (0,2) and points of intersection of the parabolas
x^2 +2x+3y+4=0 and x^2 -3x+y+3=0

Find an equation of the curve that passes through the point
and has the given slope. (Enter your solution as an
equation.)
(0, 4), y' =
x
6y
2. Find the particular solution of the differential equation
that satisfies the initial condition. (Enter your solution as an
equation.)
Differential Equation Initial Condition
y(1 + x2)y' − x(7 + y2) = 0
y(0) =
3

1.) Find the standard form of the equation of the parabola with
the given characteristic(s) and vertex at the origin.
Horizontal axis and passes through the point (−4, 7)
2.) Find the standard form of the equation of the parabola with
the given characteristics.
Vertex: (5, 1); focus: (3, 1)

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