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What is the equation of the parabola that has a vertex at # (56, -2) # and passes through point # (53,-9) #?

Answer 1

Isaiah Anthony

#y = -7/9 (x-56)^2 -2#

The general form of the equation is

# y = a(x-h)^2 + k#

Given #color(blue)(h = 56), color(green)(k = -2)#

#color(red)(x = 53) , color(purple)(y = -9)#

Substitute into the general form of the parabola

#color(purle)(-9) = a((color(red)(53)-color(blue)(56))^2 color(green)(-2)# #-9 = a(-3)^2-2#

#-9 = 9a -2#

Solve for #a#

# -9 + 2 = 9a#

#-7 = 9a #

#-7/9= a#

The equation for parabola with the given condition will be

graph{y= -7/9 (x-56)^2 -2 [-10, 10, -5, 5]}

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Answer 2

Avery Alexander

To find the equation of the parabola with a vertex at ((h, k)) and passing through a point ((x_1, y_1)), we can use the standard form of the quadratic equation:

[ y = a(x - h)^2 + k ]

Given that the vertex is ((h, k) = (56, -2)) and the point is ((x_1, y_1) = (53, -9)), we can substitute these values into the equation:

[ -9 = a(53 - 56)^2 - 2 ]

[ -9 = a(-3)^2 - 2 ]

[ -9 = 9a - 2 ]

[ -9 + 2 = 9a ]

[ -7 = 9a ]

[ a = \frac{-7}{9} ]

So, the equation of the parabola is:

[ y = \frac{-7}{9}(x - 56)^2 - 2 ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.