Quadratic Equations
Math ⇒ Algebra
Quadratic Equations starts at 8 and continues till grade 12.
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See sample questions for grade 9
A ball is thrown upwards and its height h (in meters) after t seconds is given by h = -5t² + 20t + 2. What is the maximum height reached by the ball?
Find the value of the discriminant for the equation 2x² + 3x + 1 = 0.
If one root of the equation x² + px + 12 = 0 is 3, what is the value of p?
If the equation x² + bx + c = 0 has roots 2 and 5, what is the value of c?
If the product of the roots of a quadratic equation is negative, what can you say about the signs of the roots?
If the quadratic equation 2x² + kx + 8 = 0 has equal roots, what is the value of k?
If the roots of a quadratic equation are 4 and -2, write the equation in standard form.
A ball is thrown upwards and its height h (in meters) after t seconds is given by h = -5t² + 20t + 2. What is the maximum height reached by the ball?
The roots of the equation x² + 2x + 1 = 0 are: (1) 1 and -1 (2) -1 and -1 (3) 1 and 1 (4) 0 and -2
Which method can be used to solve any quadratic equation? (1) Factoring (2) Completing the square (3) Quadratic formula (4) All of the above
Which of the following equations has two distinct real roots? (1) x² + 2x + 1 = 0 (2) x² - 4 = 0 (3) x² + 4 = 0 (4) x² = 0
Which of the following is a necessary condition for a quadratic equation to have two equal real roots? (1) Discriminant > 0 (2) Discriminant = 0 (3) Discriminant < 0 (4) Discriminant = 1
Fill in the blank: The axis of symmetry of the parabola y = ax² + bx + c is x = __________.
Fill in the blank: The graph of y = ax² + bx + c is called a __________.
Fill in the blank: The maximum or minimum value of a quadratic function y = ax² + bx + c occurs at x = __________.
Fill in the blank: The product of the roots of the quadratic equation ax² + bx + c = 0 is __________.
True or False: The coefficient 'a' in ax² + bx + c = 0 must not be zero.
True or False: The equation x² + 4x + 4 = 0 has only one real solution.
True or False: The graph of a quadratic equation is always a straight line.
True or False: The graph of y = -x² opens upwards.
