Answer and explanation:
We khow that the standard form of a parabola is written this way:
ax^2 + bx +c
It can be factored if it has roots
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In the graph we notice that the parabola has two x-intercepts wich means two roots
Let p and q be the roots
The equation can be written as:
a (x-p) (x-q)
We can khow the value of p and q from the graph
The parabola crosses the x-axis in -6,25 and 0.5
So the equation is:
Y=a(x-0.5) (x+6.25)
a is missing but we can find it
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Replace x and y bu the coordinates of a point in the parabola
Let's take (-3;3)
3= a (3-0.5) (3+ 6.5)
3 =a* 2.5* 9.5
a= 3/(2.5*9.5) = 0.12
So the equation is :
y= 0.12(x-0.5)(x+6.5)
y= (0.12x-0.6)(x+6.5)
y= 0,12x^2 + 0.78x -0.6x- 3.9
y= 0.12x^2 +0.18x-3.9
Divide by 3 to simplify :
y= 0.4x^2+0.6x-1.3
Multiply by 10 to get rid of the decimal numbers
y= 4x^2 + 6x -13