facas9

2021-10-24

What is the equation of a quadratic function whose graph passes through $(2,0)$ , $(5,0)$ , and $(3,-8)$ ? Write your equation in standard form.

okomgcae

Skilled2021-10-25Added 93 answers

Consider the given:

The graph passes through$(2,0)$ , $(5,0)$ and $(3,-8)$ .

Let the equation is$y=a{x}^{2}+bx+c$ .

Consider the point$(2,0)$ ,

$a{\left(2\right)}^{2}+b\left(2\right)+c=0$

$4a+2b+c=0$ ... ... (1)

Consider the point$(5,0)$ ,

$a{\left(5\right)}^{2}+b\left(5\right)+c=0$

$25a+5b+c=0$ ... ... (2)

Consider the point$(3,-8)$ ,

$a{\left(3\right)}^{2}+b\left(3\right)+c=-8$

$9a+3b+c=-8$ ... ... (3)

From equation (1) and (2),

$4a+2b+c=25a+5b+c$

$4a+2b=25a+5b$

$a\u201325a=5b\u20132b$

$-7a=b$

From equation (1),

$4a+2b+c=0$

$4a+2(-7a)+c=0$

$4a\u201314a+c=0$

$-10a+c=0$

$c=10a$

Substitute the value of b and c in equation (3).

$9a+3b+c=-8$

$9a+3(-7a)+\left(10a\right)=-8$

$9a\u201321a+10a=-8$

$-21a+19a=-8$

$-2a=-8$

$a=4$

$b=-7a$

$b=-7\left(4\right)$

$b=-28$

$c=10a$

$c=10\left(4\right)$

$c=40$

Hence, The equation of quadratic function will be:

$y=4{x}^{2}\u201328x+40$

The graph passes through

Let the equation is

Consider the point

Consider the point

Consider the point

From equation (1) and (2),

From equation (1),

Substitute the value of b and c in equation (3).

Hence, The equation of quadratic function will be:

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