Graphs and Factorising
TP, AoS, &
y-intercepts
y-intercepts
x-intercepts & # of sol
Completing the square and interpreting graphs
Applications
100
Draw and label an example of a concave up and concave down parabola
*teacher draw on board*
100
Find the y-intercept: y= 2x2 - 5x - 1
y = -1
100
How many solutions are there to y = 3x2 − 6x + 5 ?
discriminant < 0 so no solutions
100
Factorise by completing the square: y = x2 + 6x + 15
y = (x + 3)2 + 6
100
A piece of wire measuring 100 cm in length is bent into the shape of a rectangle. Let x cm be the breadth of the rectangle. Use the perimeter to write an expression for the length of the rectangle in terms of x.
Length = 50 - x
200
Factorise: x2+3x+2
(x+2)(x+1)
200
Find the y-intercept: y = (2x-3)(5x+2)
y = -6
200
Determine the x-intercept(s): y = x2 − 6x + 8
x = 2, 4
200
Find the turning point of the following quadratic by first completing the square: y = x2 − 4x + 2
TP: (2, -2)
200
The sum of two numbers (both greater than or equal to zero) is 20 and x is the smaller number. Write the second number in terms of x.
y = 20 - x
300
Factorise: x2-15x+36
(x-3)(x-12)
300
Find axis of symmetry: y = 3x2+6x-5
x = -1
300
Solve the following quadratic equation: y = 5x2-x-4
x = -4/5, 1
300
Is the parabola concave up or down, and how many solutions does it have?
Concave down, 2 solutions
300
The equation for a support span is given by h=−(1/40)(x − 20)2, where h(m) is the distance below the deck of a bridge and x(m) is the distance from the left side. Determine the coordinates of the turning point of the graph.
TP: (20, 0)
400
Factorise: 2x2-x-15
(x-3)(2x+5)
400
Find turning point and state if maximum or minimum: y = x2+8x+16
Minimum, (-4, 0)
400
Solve the following using the quadratic formula:
y = 2x2 + 4x − 3
x = 0.58, −2.58
400
Describe the transformations made to the graph of y = x2 for the following quadratic: y = (x − 1)2 + 16
Translated 1 unit right and 16 units up
400
A piece of wire measuring 100 cm in length is bent into the shape of a rectangle. Let x cm be the breadth of the rectangle. Write an equation for the area of the rectangle (A cm 2) in terms of x .
A = x(50-x)
500
Factorise: 6y2+7y-5
(2y-1)(3y+5)
500
Messi kicked a soccer ball from mid-field to the goal. The height (m) of the ball can be described by the equation h = -3t2 +12. What is the maximum height reached by the ball?
12 m
500
Find the solutions to the equation: y = 3x2− 4x − 2
x = -0.39, 1.72
500
Write, in vertex form, the equation of a parabola that has been horizontally translated 3 units left and vertically translated 5 units down.
y = (x+3)2-5
500
Mbappe kicked the soccer ball. The height (m) of the ball at t seconds can be given by h =-16t2+80t+384. Find when the ball reaches the max height AND the max height.
t = 2.5 seconds, h = 544 m