Use the graph of y = 3x^2 + 6x - 7 at the right to estimate the solutions to each equation.
3x^2 + 6x - 7 = 0
Use the graph of y = 3x^2 + 6x - 7 at the right to estimate the solutions to each equation.
3x^2 + 6x - 7 = -7
Use the graph of y = 3x^2 + 6x - 7 at the right to estimate the solutions to each equation.
3x^2 + 6x - 9 = 0
Determine the roots .
\displaystyle
x^2 + 5x - 14 = 0
Determine the roots .
\displaystyle
5x^2 - 9x + 1 = 0
Determine the roots .
\displaystyle
2x^2 - 8 = 24
Determine the roots .
\displaystyle
2(x -1)^2 - 5 = 0
Complete the square to find the vertex.
\displaystyle
y = 2x^2 + 12x -14
Complete the square to find the vertex.
\displaystyle
y = 3x^2 - 15x -24
Can all quadratic relations be written in vertex form by completing the square? Justify your answer.
Without solving, determine the number of real roots it has.
y = 2x^2 -4x + 7
Without solving, determine the number of real roots it has.
y =3(x-4)(x-4)
Without solving, determine the number of real roots it has.
y = (x-3)^2
April sells specialty teddy bears at various summer festivals. Her profit for a week, P, in dollars, can be modelled by P = -0.1n^2 + 30n - 1200, where n is the number of teddy bears she sells during the week.
a) According to this model, could April earn a profit of in one week? Explain.
b) How many teddy bears would she have to sell to break even?
c) How many teddy bears would she have to sell to earn $500?
d) How many teddy bears would she have to sell to maximize her profit?
Sean and Farah have 24 m of fencing to enclose a vegetable garden at the back of their house. Determine the dimensions of the largest rectangular garden they could enclose, using the back of their house as one of the sides of the rectangle.
Give two reasons why 3x^2 + 6x + 6 cannot be a perfect square.
A rapid—transit company has 5000 passengers daily, each currently paying a $2.25 fare. For each $0.50 increase, the company estimates that it will lose 150 passengers daily. If the company must be paid at least $15 275 each day to stay in business, what minimum fare must they charge to produce this amount of revenue?