Linear Graphs and Parabola

Question 1

What is the straight line equation in gradient-y-intercept form?

Answer 1

y= mx +b

Question 2

What is the straight line equation in general form?

Answer 2

ax + by + c = 0

Question 3

What is the general form equation for a parabola?

Answer 3

y= ax*2 + bx + c

Question 4

What is the formula for gradient?

Answer 4

rise/run or y2-y1/ x2- x1

Question 5

How do you find the distance between two points?

Answer 5

Pythagoras Thereom

the square root of (x2-x1 squared) plus (y2-y1 squared)

Question 6

What is the formula for midpoint?

Answer 6

x1 + x2/2, y1 + y2/2

Question 7

What are the two rules for general form?

Answer 7

no fractions and the x must be positive

Question 8

How do you find the equation of a line passing through two points and with what formula?

Answer 8

step 1- find the gradient

step 2- use formula y-y1 = m(x-x1)

Question 9

Find the equation of the line passing through 8,11 and -1, 2

Answer 9

y=x+3

Question 10

How do you know if two points fall on a line?

Answer 10

A point lies on a line if the co-ordinates of the point satisfy the equation of the line.(substitution method)

Question 11

How do you know if two points are parallel?

Answer 11

They have the same gradient

Question 12

How do you know if two points are perpendicular?

Answer 12

Have the reciprocal value and opposite sign- when the gradients of either lines, m1 and m2, are multiplied they give -1

Question 13

Convert 3x + 2y - 4 = 0 to gradient-y-intercept form

Answer 13

2y= -3x +4
y= -3/2 + 2

Question 14

What is the formula to find the axis of symmetry of a parabola?

Answer 14

-b/2a

Question 15

How do you find the y-intercept of a parabola?

Answer 15

let x+0
example: 
y= 3x*2 +2x -5
y+ (0) + (0) -5
therefore, y= -5

Question 16

How do you find the x-intercept of a parabola?

Answer 16

use -b+- the square root of b*2 -4ac all over 2a and allow y to = 0

Question 17

How do you find the coordinates of the vertex of a parabola?

Answer 17

First find the x value using the axis of symmetry and then substitute the x-value into the original equation.

Question 18

If a>0 does the graph concave up or down?

Answer 18

upwards- the parabola has a minimum turning point

Question 19

If a<0 does the graph concave up or down?

Answer 19

downwards- the parabola has a maximum turning point