Studdy AI Logo
Math

QuestionFind the zeros of the function f(x)=4x2+6x+1f(x)=4x^{2}+6x+1 using the quadratic formula. What are the xx-intercepts?

Studdy Solution

STEP 1

Assumptions1. The function is a quadratic function given by f(x)=4x+6x+1f(x)=4x^{}+6x+1 . We are asked to find the zeros of the function using the quadratic formula3. The quadratic formula is given by x=−b±b−4acax=\frac{-b\pm\sqrt{b^{}-4ac}}{a} for a quadratic equation ax+bx+c=0ax^{}+bx+c=0
4. The xx-intercepts of the function are the xx values where f(x)=0f(x)=0, which are also the zeros of the function

STEP 2

First, we need to identify the coefficients aa, bb, and cc from the quadratic function f(x)=4x2+6x+1f(x)=4x^{2}+6x+1.
a=4a=4, b=6b=6, and c=1c=1

STEP 3

Now, we can substitute these values into the quadratic formula to find the zeros of the function.
x=−b±b2−ac2ax=\frac{-b\pm\sqrt{b^{2}-ac}}{2a}

STEP 4

Substitute a=4a=4, b=6b=6, and c=1c=1 into the formula.
x=−6±62−4∗4∗12∗4x=\frac{-6\pm\sqrt{6^{2}-4*4*1}}{2*4}

STEP 5

Calculate the value under the square root, known as the discriminant.
Discriminant=b2−4ac=2−4∗4∗1=36−16=20Discriminant = b^{2}-4ac =^{2}-4*4*1 =36-16 =20

STEP 6

Substitute the discriminant back into the quadratic formula.
x=−6±208x=\frac{-6\pm\sqrt{20}}{8}

STEP 7

implify the expression under the square root.
20=25\sqrt{20} =2\sqrt{5}

STEP 8

Substitute this back into the quadratic formula.
x=−6±258x=\frac{-6\pm2\sqrt{5}}{8}

STEP 9

implify the expression by dividing each term in the numerator by2.
x=−3±54x=\frac{-3\pm\sqrt{5}}{4}These are the zeros of the function.

STEP 10

The xx-intercepts of a function are the xx values where f(x)=0f(x)=0. For a quadratic function, these are the same as the zeros of the function.
Therefore, the xx-intercepts are x=−3+54x=\frac{-3+\sqrt{5}}{4} and x=−3−54x=\frac{-3-\sqrt{5}}{4}.
So, the correct choice is B. The zeros and the xx-intercepts are the same. They are x=−3+54x=\frac{-3+\sqrt{5}}{4} and x=−3−54x=\frac{-3-\sqrt{5}}{4}.

Was this helpful?

Studdy solves anything!

banner

Start learning now

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

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord