Question

Can someone please help me with these questions?

Answer 1

QUESTION 1

The given function is

$y = - 6x - 13$

The domain of this function refers to all values of x for which y is defined.

The given function is defined for all real values of x.

The domain is all real numbers.

The correct answer is A

QUESTION 2

The equation in column 1 is

$y = - 2 {x}^{2} - 4x + 12$

We obtain the vertex form as follows;

$y = - 2( {x}^{2} + 2x) + 12$

$y = - 2( {x}^{2} + 2x + {1}^{2}) - - 2 {(1)}^{2} + 12$

$y = - 2({(x + 1)}^{2}) + 2 + 12$

$y = - 2({x + 1)}^{2} + 14$

The x-value of the vertex is -1.

The equation in column 2 is

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

We can also find the x-value of the vertex using the formula,

$x = - \frac{b}{2a}$

$x = - \frac{ - 4}{2(1)}$

$x = 2$
The correct answer is

B) The value found in column #1 is less than the value found in column #2

QUESTION 3

The height of the ball is modeled by

$h(t) = - 16 {t}^{2} + 64t$
where t equals the time in seconds and h(t) represents the height of the ball at time t seconds.

The axis of symmetry can be found using the formula,

$t = - \frac{b}{2a}$

$t = - \frac{ 64}{2( - 16)}$

$t = 2$

The correct answer is

A) t=2; it takes 2 seconds to reach maximum height and 2 seconds to fall back to the ground

QUESTION 4

The equation of axis of symmetry is given by the formula,

$x = - \frac{b}{2a}$

For the axis of symmetry of a given quadratic function to be zero, then the b-value of quadratic function should be zero.

The only equation from the given options whose b-value is zero is

$y = {x}^{2} + 2$

The axis of symmetry is

$x = - \frac{0}{2(1)}$

$x = 0$

The correct answer is C