We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

3. What is the focus of the parabola?

y=−14x2−x+3

Enter your answer in the boxes.

(__,__)

4. The equation of a parabola is y=12x2+6x+23 .

What is the equation of the directrix?

y = 5.5

y = 4.5

y = 2

y = 0.5

5. The equation of a parabola is 132(y−2)2=x−1 .

What are the coordinates of the focus?

(1, 10)

(1, −6)

(9, 2)

(−7, 2)

sii1lver May 11, 2018

#1**+1 **

Please post one question at a time.

3. What is the focus of the parabola?

y=−14x2−x+3

Enter your answer in the boxes.

\(y=−14x^2−x+3\\ y-3=−14(x^2+\frac{1}{14}x)\\ \frac{-1}{14}(y-3)=x^2+\frac{1}{14}x\\ \frac{-1}{14}(y-3)+\frac{1}{784}=x^2+\frac{1}{14}x+\frac{1}{784}\\ \frac{-1}{14}(y-3-\frac{1}{56})=(x+\frac{1}{28})^2\\ (x+\frac{1}{28})^2=\frac{-1}{14}(y-3\frac{1}{56})\\ (x+\frac{1}{28})^2=4*\frac{-1}{56}(y-3\frac{1}{56})\\\)

concave down parabola

\(Vertex=(\frac{-1}{28},3\frac{1}{56})\\ Axis\; of \;symmetry:\quad x=\frac{-1}{28}\\ focal\;length=\frac{1}{56}\\ focus=(\frac{-1}{28},3\frac{1}{56}-\frac{1}{56})\\ focus=(\frac{-1}{28},3)\\ \)

Here is the graph

Melody May 11, 2018