Question

Which of the following equations describes the graph?

Answer 1

The equation of the graph given is determined as y = 2x² - 3 (option C).

How to determine the equation of the graph given?

The equation of the graph given is determined by applying general equation of a parabola as shown below;

y = a (x - h)² + k

where;

• (h, k) is the vertex of the parabola

from the graph, x - coordinate of the vertex , h = 0

the y - coordinate of the vertex, k = - 3

y = a (x - h)² + k

y = a (x - 0)² - 3

y = ax² - 3

Using a root of the function, the value of "a" is calculated as;

x = -1.2 or 1.2

at x = 1.2 , y = 0

y = ax² - 3

0 = a(1.2²) - 3

0 = 1.44a - 3

1.44a = 3

a = 3 / 1.44

a ≈ 2

The equation becomes;

y = ax² - 3

y = 2x² - 3 (option C).

Answer 2

The equation that represents the graph is:

`y=2x^2-3`

Explanation:

We know that the general quadratic equation of the type:

`y=ax^2+bx+c`

is a upward or a downward parabola depending on a.

If a>0 then the parabola is a upward open parabola.

and if a<0 then the parabola is a downward open parabola.

Hence, the option:

`y=-2x^2-3\\\\and\\\\y=-2x^2+3`

Hence, the two options are discarded as there leading coefficient is negative but the parabola is open downward.

Hence, we are left with

`y=2x^2+3\ and\ y=2x^2-3`

From the graph, we have when x=0 we have f(0)= -3

Hence, the only option we are left with is:

`y=2x^2-3`

( Since, in the option:

`y=2x^2+3` at x=0 we have y=3≠ -3 )