PLEASE HELP FOR THE LOVE OF GOD

Solved

Show answers

Ответ:

thisbegaby

27.11.2021

Mathematics

$f(x)=-4(x+\frac{3}{4})^2+\frac{13}{4}$

Step-by-step explanation:

The Vertex form of a quadratic function is f(x)=a(x-h)^2+k , where (h,k) is the vertex of the parabola, and the sign of the coefficient indicates if the parabola opens down or opens up.

The Standard form of a quadratic function is f(x)=ax^2+bx+c , where the sign of the coefficient indicates if the parabola opens down or opens up.

To transform a quadratic function from Standard form to Vertex form, you need to complete the square.

Given the quadratic function $f(x)=-4x^{2}-6x+1$ :

Indentify a:

a=-4

Factor out -4:

$f(x)=-4(x^2+\frac{3}{2}+\frac{1}{4})$

Take the coefficient b and add and subtract $(\frac{b}{2})^2$ to keep the balance:

$(\frac{b}{2})^2=(\frac{\frac{3}{2}}{2})^2=(\frac{3}{4})^2$

$f(x)=-4(x^2+\frac{3}{2}x+(\frac{3}{4})^2)-\frac{1}{4}-(\frac{3}{4})^2)$

$f(x)=-4(x^2+\frac{3}{2}x+(\frac{3}{4})^2)) +1+(\frac{9}{4})$

Now rewrite the expression in the form $-4(x+\frac{b}{2})^2$ , this is:

$f(x)=-4(x+\frac{3}{4})^2+\frac{13}{4}$

0,0(0 оценок)

Ask your question to the AI advisor

Ai-bot is an expert in any field and is the perfect companion for reliable and useful answers and advice on a variety of topics, including science, history, technology, art, sports, health, culture and more.

Ask your question

More tips

Answers on questions: Mathematics

Ask an AI advisor a question

I want advice