coordinate geometry is confusing!! help me!! i hv alot of qns!!?

Question

1) what is gradient? of y?
2) what is y=mx+c
3) what is y=ax(square)+bx+c
4)what is quadratic curve and a is not equal to 0
5) what is y-intercept?

okay i know i hv alot of qns but pls try to help me...thx :))

Answer 1

1) The gradient of y is another way of saying the slope of y. It measures how much y changes over a certain space. For example, if you take two points, 0,0 and 1,1, then the gradient of y=1 (over 1 space, up 1 space: 1/1=1). If the two points were 0,0 and 2,1 then the gradient would be .5 (over 2 spaces, up 1 space: 1/2=.5)

2) y=mx+c is the formula for a straight line, shifted from the 0,0 point by 'c' spaces.

3) ax(square)+bx+c=0 is known as the quadratic equation. It will always yield two answers when a is not equal to 0. The answers represent the spots where a curve crosses the x-axis of a graph. Imagine the letter A upside down, and pretend that the horizontal line is the x-axis. The quadratic equation can be utilized to determine the location where the horizontal line connects with the two diagonal lines.

4) If a is not equal to 0, the quadratic curve comes out looking like the letter V with a rounded bottom instead of a sharp point. Where the curve is on a graph depends on the variables a, b and c.

5) the y-intercept is the spot on a graph where a curve or line crosses the y-axis.

Answer 2

Gradient
- Use a graphpaper and draw a x and y axis.
- Draw a straighline in the graph paper.. no worry how your draw, but make sure it is a straigh line, that is not necessary cutting the 0,0
- The gradient is the measure of how sloppy in your straight line above. negative gradient meaning the line is heading downwards as x is increasing. Positive gradient is the line heading upwards as x increasing. If 0 then it will be parallel to x axis. if infinity... then will be parallel to y axis.

Y=mx + C
- As refering to the straight line that you have drawn just now....
- Y=Mx + C is the linear equation whereby it develop for your to get the number in Y coordinate if there is X coordinate, or vice versa. It is use to get the answer if your graph paper is limited space.
- M is the gradient
- C is the value of Y Coordinate if X is equals to 0

Y= ax^2 + bx + c
- is a quadratic equation.
- now.. from the same graph paper which having the straight line in it.
- draw a smiley face or sad face... cuting or not cutting through the x axis. that will be the quadratic equation.
- this enable you to find the coordinate of Y if given value in X along that line, if a,b and c is known.

if a is not equal to 0,
- if 0, then will come back to your 1st question above.
- two interpretation here... if not 0, then it is either negative value or positive value.
- if a is a positive value, then you will have a smiley face.
- if a is a negative value, you will have a negative face.

y-intercept
- generally is the value of y if x = 0

Answer 3

S.L.Loney's book on two dimensional coordinate geometry answers all your questions. (OR any other standard book you are using in your school). Incidentally, recheck on the completeness/correctness of questions 1 and 4. Regarding other questions, y = mx + c represents a straight line whose slope(gradient) = m = tangent of the angle it makes with the x axis AND c is the intercept cut off the y axis (distance between the origin and the point where the straight line cuts the y axis. It could be +ve OR -ve, depending on whether the line cuts the y axis above or below the origin. If the line passes through the origin, then c =0). Question 3: The equation represents a curve of the second degree and its shape (conic section) should be a parabola. For a hyperbola (the sign and power of y is required to be appropriately adapted, along with appropriate values of the coefficients and constants). The equation would represent a straight line! (if a = 0). Relative numerical values of the coefficients a, b, & c also play an important part. If the degree of the other variable, y, is also raised to two, a hyperbola, an ellipse or a circle, can be obtained by adjusting the eccentricity of the curve. Also, since, y, is of the first degree, the curve (parabola) will be uniformly distributed about the y axis. Question 5: Already answered as part of answer to question 2. PLEASE NOTE: I STUDIED COORDINATE GEOMETRY IN 1963 - 64, AND THEREFORE, MY ANSWER MAY HAVE SOME INACCURACIES, DUE TO FAILING MEMORY. PLEASE LET YOUR CURRENT TEACHER CORRECT THIS, AS NECESSARY, IN CASE SOME MISTAKES ARE DETECTED. SORRY, I COULD NOT EVEN BORROW A TEXT BOOK ON COORDINATE GEOMETRY. I TRIED TO OBTAIN ONE BUT NONE WAS AVAILABLE IN THIS AREA. OTHERWISE, I SHOULD HAVE GIVEN YOU A SIMPLER AND 100% ACCURATE ANSWER.

Answer 4

I havent heard the term gradient so much but I have heard the term slope

1)or rise over run meaning how fast the function moves up/down in the same space as right/left

so if the two points are say 0,0 and 4, 8

the rise is 8 (8-0) and the run is 4 (4-0)

3) so rise over run would equals 8/4 = 2 or , the function moves up 2 for every one over. the would be the "m" in the y=mx+c

5)the c is the y-intercept or where the line crosses the x axis. so in this case with these to points

y = 2x+0 2 = rise/run or gradient, 0 equals the point of crossing the x axis.

chew on that for a bit

Answer 5

1) Rise / Run
2) Is the base formula of a linear function, m = Gradient, c = Y-value at Y-intercept
c) Is the base formula of a quardratic function
d) A curve from a formula of c) where a is not 0
e) Where the line crosses the Y-axis