Respuesta :

[tex]\bf \textit{x-intercepts or "solutions"}= \begin{cases} (-2,0)\implies x=-2\implies &x+2=0\\ (4.6,0)\implies x=4.6\implies &x-4.6=0 \end{cases}[/tex]

that simply means, the two factors for that equation will then be (x+2)(x-4.6)

for the f(x) function or "y" for that matter, that simply means

y = a(x+2)(x-4.6) which give us  y = a(x²-2.6x-9.2) if we do some FOIL on it

so.. what the dickens is the coefficient "a" then?

well, we have the y-intercept, we know is (0, 1.5)   that simply means when x = 0, y = 1.5  well, let's use that point, since it's a point on the parabola

[tex]\bf y=a(x^2-2.6x-9.2)\implies 1.5=a(0^2-2.6(0)-9.2) \\\\\\ 1.5=-9.2a\implies \cfrac{1.5}{-9.2}=a\implies -0.163 \approx a = -\cfrac{15}{92}\\\\ -----------------------------\\\\ thus \\\\\\ y=-0.163(x^2-2.6x-9.2)\\\\\\ y=-0.163x^2+0.4238x+1.4996 \\\\\\ \textit{or you can just convert them all to fractions and get} \\\\\\ y=-\cfrac{15}{92}x^2+\cfrac{39}{92}x+\cfrac{3}{2}[/tex]
adioabiola

The equation of the parabola as described is; y = (1.5/9.2)(x² - 2.6x -9.2)

Equation of a parabola

Since the roots of the parabola are as described;

The equation of a parabola in the form as described is;

y = a(x² -2.6x -9.2)

Hence, upon substitution of the y-intercept; (0,1.5), it follows that;

  • a = 1.5/9.2

Ultimately, the equation of the parabola is; y = (1.5/9.2)(x² - 2.6x -9.2)

Read more on equation of a parabola;

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