QuestionFind the real zeros of the function $f(x)=x^{2}+10x+22$ using the quadratic formula. What are the x-intercepts?

Studdy Solution

STEP 1

Assumptions1. The function is a quadratic function given by $f(x)=x^{}+10x+22$ . We are to find the real zeros of the function using the quadratic formula.
3. The quadratic formula is given by $x = \frac{-b \pm \sqrt{b^{}-4ac}}{a}$ , where $a$ , $b$ , and $c$ are the coefficients of the quadratic equation $ax^{}+bx+c=0$ .
4. The real zeros of the function are also the x-intercepts of the graph of the function.

STEP 2

Identify the coefficients of the quadratic equation. In this case, $a=1$ , $b=10$ , and $c=22$ .

STEP 3

Substitute the coefficients into the quadratic formula.
$x = \frac{-b \pm \sqrt{b^{2}-ac}}{2a}$ $x = \frac{-10 \pm \sqrt{10^{2}-(1)(22)}}{2(1)}$

STEP 4

implify the expression under the square root.
$x = \frac{-10 \pm \sqrt{100-88}}{2}$

STEP 5

Calculate the value under the square root.
$x = \frac{-10 \pm \sqrt{12}}{2}$

STEP 6

Note that the square root of12 is not a whole number, so we can simplify it by factoring12 into4 and3, and taking the square root of4.
$x = \frac{-10 \pm2\sqrt{3}}{2}$

STEP 7

implify the expression by dividing each term in the numerator by2.
$x = -5 \pm \sqrt{3}$ These are the real zeros of the function.

STEP 8

The x-intercepts of a function are the x-values for which $f(x) =0$ . In other words, they are the real zeros of the function.Therefore, the x-intercepts of the function are $x = -5 + \sqrt{3}$ and $x = -5 - \sqrt{3}$ .

STEP 9

Select the correct choiceB. The zeros and the x-intercepts are the same. They are $x = -5 + \sqrt{3}$ and $x = -5 - \sqrt{3}$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms