SOLUTION: Please help me with this equation. Express Each equation of no. 1 to 3 in the form a(x+b)^2+c Sketch the graph of y against x.for each graph,give the coordinates of the points

Question 983056: Please help me with this equation.
Express Each equation of no. 1 to 3 in the form a(x+b)^2+c
Sketch the graph of y against x.for each graph,give the coordinates of the points where it intercepts the axes (if any),the gradient of the graph where it cuts the y-axis,the coordinates of the maximum or minimum turning point.draw also its axis of symmetry and write down the equation of the axis.
1. y=3-15x-3x^2
2. y=16-x-x^2
3. y=-x^2-4x-7

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Please help me with this equation.
Express Each equation of no. 1 to 3 in the form a(x+b)^2+c
Sketch the graph of y against x.
For each graph:
a) give the coordinates of the points where it intercepts the axes (if any),
b) the gradient of the graph where it cuts the y-axis,
c) the coordinates of the maximum or minimum turning point.
d) draw also its axis of symmetry and write down the equation of the axis.
-----
I'll do the 1st one::
1. y = 3-15x-3x^2
y = -3(x^2+5x-1)
Complete the square on x^2 + 5x + 1
=======
y = -3[x^2+5x+(5/2)^2]+3+3(25/4)
--------
y = -3(x+(5/2))^2 + (89/4)
--------
a) give the coordinates of the points where it intercepts the axes (if any),
Ans: y-intercept (0,3)
x-intercepts::
Solve 3x^2 + 15x -3 = 0 using the quadratic formuls
-------
b) the gradient of the graph where it cuts the y-axis,
Ans:
y' = -6x-15
y'(0) = -15
--------------------
c) the coordinates of the maximum or minimum turning point.
Solve::
-6x-15 = 0
x = -5/2
y = f(-5/2) 89/4
d) draw also its axis of symmetry and write down the equation of the axis.
Ans:
axis:: x = -5/2
====================
Cheers,
Stan H.
-------------
RELATED QUESTIONS
a) Express the equation in the form y = mx + b, b) find the slope and the y-intercept... (answered by mananth)

1. write an equation of the line containing (6, 5) and having slope 3/4. a. express... (answered by oscargut)

Please help me solve this equation: Express each of the following systems of equations... (answered by Edwin McCravy)

Hi, I needed help with my precalc honors summer work, and I was wondering if someone... (answered by lwsshak3)

Dear Sir/Madam. Can you please help me solve the following multi-part problem? I tried (answered by josgarithmetic)

This is my question:express each of the following in the form y = a(x - h)^2 + k. Hence... (answered by kietra)

Please help me solve this equation: Sketch the graph of G(x) = -(x -... (answered by josgarithmetic)

1.Sketch the curves of the following functions (a) f(t)= 4t^2- 12t (b) f(x)= 4-2x-x^2... (answered by rothauserc)

I need help with this please :) equation is f(x)= x^2 - 4x - 3 a)Graph y=f(x) in... (answered by stanbon)