Mathematics: What are the x-intercepts of the graph of the function f(x) = x2 + 5x − 36? a. (−4, 0) and (9, 0) b. (4, 0) and (−9, 0) c. (−3, 0) and (12, 0) d. (3, 0) and (−12, 0)

Well, put the numbers into the fractions, multiply, then get the number out (don t get it? here s an example):...

What are the x-intercepts of the graph of the function

beccakubas

09.06.2020

we have

$f(x)=x^{2} +5x-36$

we know that

The x-intercepts are the values of x when the value of the function is equal to zero

Equate the function to zero and solve for x

$x^{2} +5x-36=0$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$x^{2} +5x=36$

Complete the square. Remember to balance the equation by adding the same constants to each side.

$(x^{2} +5x+6.25)=36+6.25$

$(x^{2} +5x+6.25)=42.25$

Rewrite as perfect squares

$(x+2.5)^{2}=42.25$

$(x+2.5)^{2}=42.25\\(x+2.5)=(+/-)\sqrt{42.25} \\(x+2.5)=(+/-)6.5\\x1=+6.5-2.5=4\\x2=-6.5-2.5=-9$

therefore

the x-intercepts are the points $(4,0)\ and\ (-9,0)$

the answer is the option

B. (4, 0) and (−9, 0)

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