Question

Complete ye table of values

Answer 1

a)
Missing values

x = -2 y = 5

x = 0 y = - 3

x = 1 y = - 1

x = 3 y = 0

b)

i) A

ii) - 1.75

iii) x = 1 + √5 and x = 1 - √5

In decimal that would be
x = 3.23606 and x = −1.23606

I am not sure which form they want it in

Explanation:

Given function is
y = x² - 2x - 3

a) To find the missing y values, plug in the corresponding value of x and solve for y

x = -2 ==> y = (-2)² -2(-2) - 3 y = = 4 + 4 - 3 or y = 5
x = 0, y = 0² -2(0) - 3 = - 3
x = 1, y = 1² -2(1) - 3 = 1 - 2 -3 = - 4
x = 3, y = 3² - 2(3) - 3 = 0

b)

i) Graph A(blue) matches the function expression; when x = 1, y = -4 in this curve

ii) Estimate the value of y when x = 2.5

Plug in x = 2.5 into the function

y = (2,5)² -2(2.5) - 3 = 6.25 - 5 - 3 = - 1.75

c) Find the value of x at y =1

When y = 1, we get
x² - 2x - 3 = 1

Moving 1 to the left side gives

x² - 2x - 4 = 0

This is a quadratic equation which can be solved using the quadratic equation. There are calculators for this to ease your pain

But if doing manually

A quadratic equation of the form
ax² + bx + c = 0 will have the solutions

`x_(1,\:2)=(-b\pm √(b^2-4ac))/(2a)`

In the given expression,
a = 1, b = -2 and c = -4

Let's calculate the individual terms in the quadratic formula and combine everything to solve

b² - 4c = (-2)² -4(1)(-4)
= 4 + 16

= 20

`√(b^2- 4ac) = √(20) = √(4 \cdot 5) = 2√(5)`

Therefore the two values of x are

`x_1=(-\left(-2\right)+2√(5))/(2\cdot \:1)\\\\= (2 + 2√(5))/(2)\\= 1 + √(5)\\\\`

`x_2=(-\left(-2\right) - 2√(5))/(2\cdot \:1)\\\\= (2 - 2√(5))/(2)\\\\= 1 - √(5)\\\\`

So the values of x when y = 1 are

`x=1+√(5),\:x=1-√(5)`

Answer 2

Answer: Here you go champ.

Explanation:

a.) FROM LEFT TO RIGHT

5, -3, -4, 0

b.) Curve A

ii.) about -1.75

iii.) 3.236, -1.236