Discriminant and Nature of Roots
How many zeros (x-intercepts) can a quadratic function have?
What is 2, 1, or none?
Factorise 5x2-9x-2.
What is (5x+1)(x-2)?
Solve 6x2-11x-10=0.
What is
x=-2/3 or x=5/2
?
At what point will the graph of the given function cross the y-axis?
y=2x^2-5x-3
(0,-3)
A decorative arch is to be constructed for a party. It is parabolic with a 1 m long horizontal row of light below the highest point. If the parabola can be modelled using the equation
y=-2.8x(x-2)
, what is the height of the horizontal row of light?
2.1 m
What is the value of the discriminant of x2+5x-1=0?
What is 29?
What are the vertex of the quadratic function y = 5(x-3)2 - 2?
What is (3,-2)?
Factorise and solve 12a2-11a-15=0.
What is (3x-5)(4x+3)=0 and x=5/3 or x=-3/4?
What is the equation of the axis of symmetry of
y=3x^2-24x+1
x=4
As part of a confidence course, a rope is hung from points 6 m apart on a bar. It forms a parabolic curve with lowest point 2 m below the bar. Tane is standing midway between one of the point of attachment and and the point above the rope's lowest point. How far below his feet is the rope?
1.5 m
How many times will the graph of y=2x2+x+3 cross the x-axis? Show analytical work.
What is (1)2-4(2)(3)=-23? What is None?
The quadratic function has its vertex at (-5,1) and passing through (-6,-1).
Write the function in the vertex form y=a(x-h)2+k.
What is y=-2(x+5)2+1?
Solve
(x^2+2x-8)/(x^2-x-2)=3.
Show algebraic work.
What is x=1/2?
For what value of a will the given function have a maximum value of 21?
y=ax^2-16x+5
-4
A very large parabolic fish tank in an aquarium is modelled by the function
y=x(x-3)
, where y is the depth of the tank in metres below the rim. The bottom of the tank will be filled to a level 2 m below the rim. Find the width of the top surface of the shingle?
1 m
Find all possible value(s) of b so that x2+bx+4=0 has exactly one solution.
What is
+-4?
A quadratic functions has the zeros -3 and 5 and y-intercept of -45. Write the function in x-intercept form.
What is y=3(x-5)(x+3)?
The equation has only one real solution. Find the value of x.
(x+2)-3sqrt(x+2)-4=0
What is x=14?
At what point will the given function cross the x-axis?
y=-5x^2-x+2
-0.74 or 0.54
A feature of a skateboard park is to be modelled on a parabolic shape. It has a width of 10 m and its greatest depth is 0.5 m. If the ground level is represented by the x--axis and the y-axis is the left edge of the curved surface, calculate the equation of the parabola.
y=0.02x(x-10)
Find the possible values of d if real solutions exist for x2+5x-1-d(x2+1)=0
What is
-2.69<x<2.69
?
The shape of a tunnel can be modelled by a parabola. The maximum height 6m, and at the ground level, its width is 12m. Find the equation of the parabola in y=ax2+bx+c form.
What is
y=-1/6 x^2+2x
(when center at (6,0))?
or
y=-1/6 x^2+6
(when center at (0,0))
Solve 10x4-13x2+4=0. Support answer with algebraic working.
What is
x=+-0.894
x=+-0.707
For what value(s) of p will the given function have its minimum value of -36?
y=(x+3p)(x-p)
p=+-3
An engineer is designing a tunnel which will become a walkway within the concrete walls of a large power station. The cross-section of the tunnel is in the shape of a parabola with its floor starting 2m from the left side of the concrete wall. The tunnel will be 6 m wide with highest point of 4.5 m above the floor. If a horizontal ceiling 3m wide is to be built centrally on the tunnel, how high will it be above the floor?
3.375 m