Quadratic Equations
Math ⇒ Algebra
Quadratic Equations starts at 8 and continues till grade 12.
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See sample questions for grade 12
A ball is thrown upwards and its height h (in meters) after t seconds is given by h = -5t² + 20t + 2. After how many seconds will the ball hit the ground?
A quadratic equation has roots 2 and -3. Write the equation in standard form.
Describe the effect on the graph of y = x² if the equation is changed to y = -x².
Find the discriminant of the equation 2x² - 4x + 3 = 0.
If one root of the quadratic equation x² + px + 12 = 0 is 3, what is the value of p?
If the quadratic equation x² + bx + 16 = 0 has roots that are reciprocals of each other, what is the value of b?
If the roots of the equation 2x² + 5x + 3 = 0 are α and β, find the value of 1/α + 1/β.
A ball is thrown upwards and its height h (in meters) after t seconds is given by h = -5t² + 20t + 2. After how many seconds will the ball hit the ground?
Which of the following equations has complex roots?
(1) x² + 2x + 1 = 0
(2) x² + 4x + 5 = 0
(3) x² - 6x + 9 = 0
(4) x² - 2x + 1 = 0
Which of the following is a quadratic equation?
(1) x² + 3x + 2 = 0
(2) 2x + 5 = 0
(3) x³ - 4x = 0
(4) 5x - 7 = 2x²
Which of the following is NOT a method to solve quadratic equations?
(1) Graphing
(2) Synthetic division
(3) Completing the square
(4) Using the quadratic formula
Which of the following methods can be used to solve a quadratic equation?
(1) Factoring
(2) Completing the square
(3) Quadratic formula
(4) All of the above
Fill in the blank: The axis of symmetry of the parabola y = 2x² - 8x + 3 is x = __________.
Fill in the blank: The product of the roots of ax² + bx + c = 0 is __________.
If the discriminant (b² - 4ac) of a quadratic equation is negative, the equation has __________ roots.
The general form of a quadratic equation is __________.
A quadratic equation has two equal real roots if and only if its discriminant is zero. True or False?
True or False: The coefficient 'a' in ax² + bx + c = 0 must be nonzero.
True or False: The equation x² + 4x + 4 = 0 has exactly one real root.
True or False: The graph of a quadratic equation is always a straight line.
