Write an equation any form for the quadratic graphed below


Asked by wiki @ in Mathematics viewed by 54 People


Write an equation (any form) for the quadratic graphed below

Answered by wiki @



The equation for the quadratic graphed in the figure is -1(x-2)^{2} +3 =0 (standard form) OR -x^{2} +4x-1 = 0 (general form)

To write the equation for the quadratic graphed below,

we will use the standard form of a quadratic function, which is

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

Where (h, k) is the vertex

From the graph, we observe that the vertex is at (2,3)

h = 2

and k =3

Now, to determine the value of a,

we will pick any suitable point (x, y) on the curve.

Using the point (3,2)

That is,

x = 3 and y = 2

Put these values into the equation y = a(x-h)^{2} +k and solve for a

We get

2 = a(3-2)^{2} +3

Then,

2 = a(1)^{2} + 3

2 = a +3\\

a =2-3

a =-1

Now, we will put the respective values of a, h, \ and \ k into the equation for the standard form of a quadratic function

That is,

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

Then,

y = -1(x-2)^{2} +3

Therefore the equation is

-1(x-2)^{2} +3 =0

This is the equation in the standard or vertex form.

This equation can be further simplified to give

y = -1(x-2)^{2} +3

y = -1(x-2)(x-2) +3

y = -1(x^{2} -2x-2x+4) +3

y = -1(x^{2} -4x+4) +3

y = -x^{2} +4x-4+3

y = -x^{2} +4x-1

Therefore, the equation is

-x^{2} +4x-1 = 0

This is the general form of the equation.

Hence, the equation for the quadratic graphed in the figure is -1(x-2)^{2} +3 =0 (standard form) OR -x^{2} +4x-1 = 0 (general form)

Learn more here: brainly.com/question/24978880


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