Mathematics: Write the equation for a parabola that has x − intercepts (−2.2, 0) and (−0.6, 0) and y − intercept (0,3.3). URGENT

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Write the equation for a parabola that has x − intercepts

babygirlslay109

31.01.2022

$\bold{y=2.5x^2+7x+3.3}$

Step-by-step explanation:

Given:

Parabola with

x − intercepts (−2.2, 0) and (−0.6, 0)

and

y − intercept (0,3.3)

To find:

Equation of parabola ?

Solution:

We can use factored form to find the equation of the parabola.

$y=a(x-\alpha)(x-\beta)$

Where $\alpha, \beta$ are the x intercepts.

Let use put

$\alpha = -2.2\\\beta = -0.6$

$y=a(x-(-2.2))(x-(-0.6))\\\Rightarrow y =a(x+2.2)(x+0.6)$

Now, let us put y − intercept (0,3.3) in the above equation to find the value of a.

$\Rightarrow 3.3 =a(0+2.2)(0+0.6)\\\Rightarrow 33 =a(22)(0.6)\\\Rightarrow 3 = 2a\times 0.6\\\Rightarrow a = 2.5$

So, the equation becomes:

$\Rightarrow y =2.5(x+2.2)(x+0.6)\\\Rightarrow \bold{y=2.5x^2+7x+3.3}$

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