Write an equation any form for the quadratic graphed below

Asked by wiki @ 12/07/2022 in Mathematics viewed by 61 People

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

Answered by wiki @ 12/07/2022

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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