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

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:

[tex]f(x)=(x-1)(x+4)[/tex]

[tex](x-1)(x+4)=0[/tex]

[tex]x-1=0,x+4=0[/tex]

[tex]x=1,x=-4[/tex]

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 [tex]f(x)=(x-1)(x+4)[/tex] is the fourth one.

kudzordzifrancis kudzordzifrancis · Answer 2 · 2019-05-22T15:28:57+02:00

kudzordzifrancis kudzordzifrancis

22-05-2019

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.

[tex](x - 1)(x + 4) = 0[/tex]

By the zero product property;

[tex]x - 1 = 0 \: or \: x + 4 = 0[/tex]

This implies that,

[tex]x = 1 \: or \: x = - 4[/tex]

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

The correct choice is D.

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