Question 11: Diagram above shows the graphs of the curves y = x2 + x – kx + 5 and y = 2(x – 3) – 4h that intersect the x-axis at two points. Find (a) the value of k and of h, (b) the minimum value of each curve. Solution: (a) y= x 2 … Read more

Question 9: Given that the quadratic function f(x) = 2×2 – px + p has a minimum value of –18 at x = 1. (a) Find the values of p and q. (b) With the value of p and q found in (a), find the values of x, where graph f(x) cuts the x-axis. (c) … Read more

Question 20: Find the range of values of k if the quadratic equation 3(x2 – kx – 1) = k – k2 has two real and distinc roots. Solution: 3( x 2 −kx−1 )=k− k 2 3 x 2 −3kx−3−k+ k 2 =0 3 x 2 −3kx+ k 2 −k−3=0 a=3,b=−3k,c= k 2 −k−3 In cases of two real and distinc roots, … Read more

Question 13: Show that 6x−6−2k x 2 = x 2  has no real roots if k> 1 4 . Solution: Question 14: The quadratic equation x 2 +px+q=0 has roots –2 and 6. Find (a) the value of p and of q, (b) the range of values of r for which the equation x 2 +px+q=r has no real roots. Solution: Question … Read more

Question 10: The quadratic equation x 2 −4x−1=2p(x−5) , where p is a constant, has two equal roots. Calculate the possible values of p. Solution: Question 11: Find the range of values of k for which the equation x 2 −2kx+ k 2 +5k−6=0 has no real roots. Solution: Question 12: Find the range of … Read more

Question 7: Find the value of p if one root of x 2 +px+8=0 is the square of the other. Solution: Question 8: If one root of 2 x 2 +px+9=0 is twice the other, find the values of p. Solution: Question 9: The roots of the equation 6 x 2 +hx+1=0 are α and β, whereas 3α and 3β are the roots … Read more

Question 4: If the roots of 2 x 2 +4x−1=0 are α and β, find the equations whose roots are (a)  α 2 , β 2 (b) α−β, β−α Solution: Question 5: Write and simplify the equation whose roots are double the roots of 3 x 2 −5x−1=0 , without solving the given equation. Solution: Question 6: Write and simplify … Read more

Question 1: Solve the following quadratic equations by factorisation. (a)  x 2 −5x−10=−4 (b) 3−x−2 x 2 =0 (c) 11a=2 a 2 +12 (d)  2x+7 3x−2 =x Solution: Question 2: Solve the following quadratic equations by completing the square. (a) 5 x 2 +10x−3=0 (b) 2 x 2 −5x−6=0 Solution: Question 3: Solve the following quadratic equations by using … Read more

Graphing Quadratic Function If you are asked to sketch the graph of a quadratic function, you need to show a. the shape of the graph b. the maximum/minimum point of the graph c. the x-intercept of the graph d. the y-intercept of the graph Example Sketch the curve of the quadratic function f ( x … Read more