Question

16
Select the correct answer from each drop-down menu.
What is the equation of the quadratic function represented by this table?
х
у
-3
3.75
-2
4
- 1
3.75
0
3
1
1.75
y=
(x-
02 +

Answer 1

Answer:

$y=-0.25(x+2)^2+4$

Step-by-step explanation:

General form of a quadratic function: $y=ax^2+bx+c$

(where c is the y-intercept)  

The y-intercept occurs when x = 0.  As one of the ordered pairs is (0, 3) we can say that c = 3

Therefore, $y=ax^2+bx+3$

Input two ordered pairs into the function and solve simultaneously to find a and b:

Ordered pair (-2, 4):

$a(-2)^2-2b+3=4$

$\implies 4a-2b=1$

Ordered pair (1, 1.75):

$a(1)^2+b+3=1.75$

$\implies a+b=-1.25$

$\implies a=-1.25-b$

Substituting second equation into the first and solving for b:

$4(-b-1.25)-2b=1$

$\implies -6b=6$

$\implies b = -1$

Substituting found value for b into second equation and solving for a:

$a=-1.25+1$

$\implies a=-0.25$

Therefore, the quadratic function is: $y=-0.25x^2-x+3$

To complete the square use the formula:

$y=a\left(x+\dfrac{b}{2a}\right)^2+c-\dfrac{b^2}{4a}$

$\implies y=-0.25\left(x+\dfrac{(-1)}{2(-0.25)}\right)^2+3-\dfrac{(-1)^2}{4(-0.25)}$

$\implies y=-0.25(x+2)^2+4$