Question

Which is the graph of f(x) = (x – 1)(x + 4)?

Answer 1

ANSWER

See attachment.

EXPLANATION

The given function is

f(x) = (x – 1)(x + 4).

This parabola will open upwards because the leading coefficient is positive.

The x-intercepts can be found by equating the function to zero.

$(x - 1)(x + 4) = 0$

By the zero product property;

$x - 1 = 0 \: or \: x + 4 = 0$

This implies that,

$x = 1 \: or \: x = - 4$

The graph that touches the x-axis at -4 and 1, and opens upwards is the last graph.

The correct choice is D.

Answer 2

Answer:

The fourth graph (last graph)

Step-by-step explanation:

Remember that the zeros of a function are the x-intercepts of the graph. To find the zeros we just need to set the function equal to zero and solve for x:

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

$(x-1)(x+4)=0$

$x-1=0,x+4=0$

$x=1,x=-4$

Now we know that the graph or our function intersects the x-axis at x = 1 and x = -4.

Since both x values inside the parenthesis are positive, our parabola is opening upwards.

The only graph opening upwards whose x-intercepts are x = 1 and x = -4 is the fourth one.

We can conclude that the graph of $f(x)=(x-1)(x+4)$ is the fourth one.