Question

Hich is the graph of f(x) = (x - 1)(x + 4)?
​

Answer 1

4th Graph is correct option.

Explanation:

Given Function is ,

f(x) = ( x - 1 )( x + 4 )

f(x) = x² + 3x - 4

Since, we are given a quadratic function.

So, Graph is a parabola.

Now we find the vertex of the parabola by expressing given function in standard form of parabola.

Consider,

y = x² + 3x - 4

x² + 3x = y + 4

`x^2+3x+((3)/(2))^2=y+4+((3)/(2))^2`

`(x+(3)/(2))^2=y+4+(9)/(4)`

`(x+(3)/(2))^2=y+(25)/(4)`

By comparing this equation with ( x - h )² = 4a( y - k )

where, ( h , k ) is vertex of the parabola.

⇒ Vertex of the given function =
`((-3)/(2),(-25)/(4))`

These coordinates of the vertex lie in 3rd Quadrant.

Now looking at all given graphs. Only 4th Graph has vertex in 3rd quadrant.

Therefore, 4th Graph is correct option.

Answer 2

Option D

EXPLANATION

The given function is

`f(x) = (x - 1)(x + 4)`

The graph of this function, will touch the x-axis at x=1 and x=-4.

This graph is a minimum graph.

This parabola will open up.

The correct choice is D.