Question

Select the correct answer. What is the value of a in the function’s equation?

Answer 1

Answer:

$a = -2$

Step-by-step explanation:

Given

The attached function (graph)

Required

Find a

The given function is quadratic and will be solved using:

$y = ax^2 + bx + c$

From the attachment:

$(x,y) = (-3,4)$

$(x,y) = (-2,2)$

$(x,y) = (-4,2)$

Substitute these values in $y = ax^2 + bx + c$

For: $(x,y) = (-3,4)$

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

$4 = 9a -3b + c$

For: $(x,y) = (-2,2)$

$2 = a(-2)^2 + b(-2) + c$

$2 = 4a -2b + c$

For: $(x,y) = (-4,2)$

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

$2 = 16a -4b + c$

So, we have:

$4 = 9a -3b + c$ --- (1)

$2 = 4a -2b + c$ ---- (2)

$2 = 16a -4b + c$ --- (3)

Make c the subject in (1)

$c = 4 - 9a + 3b$

Substitute $c = 4 - 9a + 3b$ in (2) and (3)

$2 = 4a -2b + c$

$2 = 4a -2b + 4 - 9a + 3b$

Collect Like Terms

$-4 + 2 = 4a - 9a-2b + 3b$

$-2 = - 5a+b$ --- (4)

$2 = 16a -4b + c$

$2 = 16a - 4b + 4 - 9a + 3b$

Collect Like Terms

$2 -4 = 16a - 9a + 3b- 4b$

$-2 = 7a -b$ --- (5)

Add 4 and 5

$-2 = - 5a+b$

$-2 = 7a -b$

--------------------------

$-2 - 2 = -5a + 7a +b - b$

$-4 = 2a$

Divide through by 2

$-2 = a$

$a = -2$