Question

Which statement describes the graph of f(x) = 4x2 + 20x + 25?

The graph does not intersect the x-axis.
The graph touches the x-axis at (–2.5, 0).
The graph intersects the x-axis at (–0.4, 0) and (0.4, 0).
The graph intersects the x-axis at (2, 0) and (5, 0).

Answer 1

2nd statement is true

Explanation:

Please use " ^ " to denote exponentation: f(x) = 4x^2 + 20x + 25.

Take a look at the second statement. If you'll substitute -2.5 for x, to find f(-2.5), you'll find that the result is 0; Thus, this second statement is true.

Answer 2

The graph touches the x-axis at (–2.5, 0).

Explanation:

Given : f(x) = 4x² + 20x + 25.

To find : Which statement describes the graph .

Solution : We have given

f(x) = 4x² + 20x + 25.

On factoring

4x² + 10x + 10x+ 25 = 0

On taking common 2x from first two terms and 5 from last two terms.

2x ( 2x + 5 ) +5 (2x + 5 ) = 0

On grouping

(2x +5) (2x +5) = 0

For 2x +5 = 0

On subtracting 5 both side

2x = -5

On dividing by 2

x =
`(-5)/(2)` = - 2.5

x = - 2.5 .

Points (-2.5 , 0)

Therefore, The graph touches the x-axis at (–2.5, 0).