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garri49 [273]
3 years ago
8

Determine the equation for the parabola graphed below?

Mathematics
2 answers:
polet [3.4K]3 years ago
8 0

Answer:

y = \frac{1}{2} x² - 2x + 1

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

From the graph (h, k) = (2, - 1), thus

y = a(x - 2)² - 1

To find a substitute a point on the curve (0, 1) into the equation

1 = 4a - 1 ( add 1 to both sides )

4a = 2 ( divide both sides by 4 )

a = \frac{2}{4} = \frac{1}{2}, hence

y = \frac{1}{2}(x - 2)² - 1 ← in vertex form

Expand the factor and simplify

y = \frac{1}{2}(x² - 4x + 4) - 1

  = \frac{1}{2} x² - 2x + 2 - 1

  = \frac{1}{2} x² - 2x + 1 ← in standard form

Vikentia [17]3 years ago
6 0
<h2>Answer:</h2>

The equation of parabola is:

                  y=\dfrac{1}{2}x^2+(-2)x+1

<h2>Step-by-step explanation:</h2>

We know that the vertex form of the equation of parabola is given by:

                 y=a(x-h)^2+k

where the vertex of the parabola is (h,k).

Now, from the graph i.e. provided to us we see that the vertex of the parabola is located at (2,-1)

i.e.

(h,k)=(2,-1)

i.e.

h=2 and k= -1

Hence, we have the equation of the parabola as:

y=a(x-2)^2+(-1)\\\\i.e.\\\\y=a(x-2)^2-1

Now, with the help of a passing through point of the parabola we may easily obtain the value of a.

The parabola passes through (0,1)

Hence, on putting x=0 and y=1 we have:

1=a(0-2)^2-1\\\\i.e.\\\\1=a\times 4-1\\\\i.e.\\\\4a-1=1\\\\i.e.\\\\4a=1+1\\\\i.e.\\\\4a=2\\\\i.e.\\\\a=\dfrac{2}{4}\\\\i.e.\\\\a=\dfrac{1}{2}

Hence, the equation of parabola will be:

y=\dfrac{1}{2}(x-2)^2-1

On expanding the square term we have:

y=\dfrac{1}{2}(x^2+(-2)^2-2\times x\times 2)-1\\\\i.e.\\\\y=\dfrac{1}{2}(x^2+4-4x)-1\\\\i.e.\\\\y=\dfrac{1}{2}x^2+\dfrac{1}{2}\times 4+\dfrac{1}{2}\times (-4x)-1\\\\i.e.\\\\y=\dfrac{1}{2}x^2+2-2x-1\\\\i.e.\\\\y=\dfrac{1}{2}x^2-2x+2-1\\\\i.e.\\\\y=\dfrac{1}{2}x^2-2x+1

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