<h2>Graph A</h2><h3>How to find the roots of the the function</h3>
The points where the graph intercepts the x-axis is the root of the function.
from the graph the points are 3.9 and 6.1
<h3 /><h3>How to write the equation of the parabola in vertex form</h3>
The vertex v is at v ( 5, -4 ) this is equivalent to v ( h, k )
the equation of parabola in vertex form is y = a ( x- h )^2 + k
y = a ( x - 5 )^2 + {-4)
substituting point ( 4, -1 ) from the graph we have:
-1 = a ( 4 - 5 )^2 - 4
-1 = a - 4
a = 3
substituting the known values to y = a ( x- h ) + k
y = 3 ( x - 5 )^2 - 4
<h3>How to write the equation of the parabola in factored form</h3>
y = 3 ( x - 5) ( x - 5 ) - 4
<h3>How to write the equation of the parabola in standard form</h3>
y = 3 ( x - 5) ( x - 5 ) - 4
y = 3 ( x^2 - 10x + 25 ) - 4
y = 3x^2 - 30x + 75 - 4
y = 3x^2 - 30x + 71
<h2>Graph B</h2><h3>How to find the roots of the the function</h3>
The points where the graph intercepts the x-axis is the root of the function.
from the graph the points are 2 and 4
<h3>How to write the equation of the parabola in vertex form</h3>
The vertex v is at v ( 3, 2 ) this is equivalent to v ( h, k )
the equation of parabola in vertex form is y = a ( x- h )^2 + k
y = a ( x - 3 )^2 + 2
substituting point ( 0, -16 ) from the graph we have:
-16 = a ( 0 - 3 )^2 + 2
-16 = a - 9 + 2
-16 = a - 7
a = -9
substituting the known values to y = a ( x- h ) + k
y = -9 ( x - 3 )^2 + 2
<h3>How to write the equation of the parabola in factored form</h3>
y = -9 ( x - 3) ( x - 3 ) + 2
<h3>How to write the equation of the parabola in standard form</h3>
y = -9 ( x - 3) ( x - 3 ) + 2
y = -9 ( x^2 - 6x + 9 ) - 4
y = 3x^2 - 54x - 81 - 4
y = 3x^2 - 54x - 85
Read more on parabolic equations here: brainly.com/question/2956567
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