Question

Which equation could generate the curve in the graph below?

Answer 1

Answer:

The answer is option 1.

Step-by-step explanation:

In order to find the equation, you have to apply Discriminant Law, D = b² - 4ac. When D < 0, the equation has no real roots (no x-intercept). When D = 0, it has 2 and equal roots (1 x-intercept). When D > 0, it has 2 distinct roots (2 x-intercept).

Option 1,

$y = 3 {x}^{2} - 2x + 1$

$D = {( - 2)}^{2} - 4(3)(1)$

$D = - 8$

$D < 0$

Option 2,

$y = 3 {x}^{2} - 6x + 3$

$D = {( - 6)}^{2} - 4(3)(3)$

$D = 0$

Option 3,

$y = 3 {x}^{2} - 7x + 1$

$D = {( - 7)}^{2} - 4(3)(1)$

$D = 37$

$D > 0$

Option 4,

$y = 3 {x}^{2} - 4x - 2$

$D = {( - 4)}^{2} - 4(3)( - 2)$

$D = 40$

$D > 0$

As you look at the graph, the curve does not meet x-axis so the discriminant must be less than 0.