Question

Write the equation of the function whose graph is shown. y = (x + )2 +

Answer 1

Quadratic form is given in the form
$y= ax^{2}+bx+c$, where a, b, and c are constants

We substitute the value (8, 12) and (5,3) in turn

$12= a(8)^{2}+b(8)+c$
$12=64a+8b+c$ ... Equation 1

$3=a(5)^{2}+b(5)+c$
$3=25a+5b+c$ ... Equation 2

Equation 1 - Equation 2 gives
$39a+3b=9$, we call this Equation 3

We also know that (5, 3) is the turning point of the curve, where the value of $x$ is given by $x=- \frac{b}{2a}$
Substitute $x=5$
$5=- \frac{b}{2a}$
$10a=-b$
$b=-10a$ ... Equation 4

Substitute Equation 4 into Equation 3
$39a+3b=9$
$39a+3(-10a)=9$
$39a-30a=9$
$9a=9$
$a=1$

Now we need to work out the value of $b$ and $c$

Substitute $a=1$ back into equation 4
$-10a=b$
$-10(1)=b$
$b=-10$

Substitute $a=1$ and $b=-10$ into either equation 1 or equation 2

$64a+8b+c=12$
$64(1)+8(-10)+c=12$
$64-80+c=12$
$c=12+80-64$
$c=28$

Hence the equation of the quadratic curve is
$y= x^{2} 10x+28$

Answer 2

Answer:

y=1(x+ -5)² +3

Step-by-step explanation:

1

-5

3