Respuesta :

The graph opens up, so “a” must be positive. This rules out choices 1 and 4. Next, find the zeroes (areas where y is 0) and see which ones match the graph.

I’ll start with option 2.
(x-2)=0
(add 2 to both sides)
x=2

(x+5)=0
(subtract 5 from both sides
x=-5

Judging by the graph, option 2 has the opposite of the zeroes needed, and thus option 3 will be the correct choice.

If you want to check option 3 further though...

(x+2)=0
x=-2

(x-5)=0
x=5

These are the correct zeroes. Option 3 is correct.

The equation of the following graph, in intercept form, which is provided in the image is,

[tex]f(x)=0.4(x+2)(x-5)[/tex]

What is parabola equation intercept form?

The intercept form of parabola can be expressed using the following expression.

[tex]f(x)=a(x-p)(x-q)[/tex]

Here, a is the constant, (p, q) are the x-values on the graph, where y is zero.

In the given graph, the point (-2,0) is the point, where the value y is zero. Here, the value of x is -2. Therefore,

[tex]p=-2[/tex]

The other point, where the value of y is zero is (5,0). Thus the value of q is,

[tex]q=5[/tex]

The value of constant a is,

[tex]a=-\dfrac{p}{q}\\a=-\dfrac{-2}{5}\\a=0.4[/tex]

Put these values in the above equation, we get,

[tex]f(x)=0.4(x+2)(x-5)[/tex]

The equation of the following graph, in intercept form, which is provided in the image is,

[tex]f(x)=0.4(x+2)(x-5)[/tex]

Learn more about the parabola equation intercept form here;

https://brainly.com/question/14228826

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