Author: Stewart Gale

Harder Solving Quadratic Equations Graphically

Q1.
(a)  Complete the table of values for y = x^2 − 5x + 3

(2)
(b)  On the grid below, draw the graph of y = x^2 − 5x + 3 for values of x from x = −1 to x = 5

(2)
(c)  Find estimates of the solutions of the equation x^2 − 5x + 3 = 0
x = .......................................................  or x = .........................................................
(2)
Q2.
 (a)  Complete the table of values for     y = x^2 – 3x + 2

(2)
(b)  On the grid, draw the graph of y = x^2 – 3x + 2 for values of x from –1 to 5
(2)

(c)  Find estimates for the solutions of the equation     x^2 – 3x + 2 = 4

...........................................................
(2)
 Q3.
 (a)  Complete the table for the values for y = 6 – x – x^2

(2)
(b)  On the grid, draw the graph of y = 6 – x – x^2 for values of x from –4 to 3

(2)
(c)  Find estimates for the solutions of the equation 6 – x – x^2 = 2
 ........................................................... 
(2)
 Q4.
 (a) Complete the table of values for y = x^2 − 2x − 1

(2)
(b) On the grid, draw the graph of y = x^2 − 2x − 1 for values of x from −2 to 4

(2)
(c) Solve x^2 − 2x − 1 = x + 3

...........................................................
(2)
Q5.
(a) Complete the table of values for y = x^2 – 2x

 (2)
(b) On the grid, draw the graph of y = x^2 – 2x for values of x from –2 to 4 

(2)
(c) Solve x^2 – 2x – 2 = 1

 

      ..............................................................................................................................
(2)
Q6.
 The diagram shows part of the graph of y = x^2 − 2x + 3

(a)   By drawing a suitable straight line, use your graph to find estimates for the solutions of x^2 − 3x − 1 = 0

 ........................................................... 
(2)
P is the point on the graph of y = x^2 − 2x + 3 where x = 2
(b)   Calculate an estimate for the gradient of the graph at the point P.

 ........................................................... 
(3)
 Q7.
 The diagram shows the graph of y = x^2 – 4x – 2

(a)  Use the graph to find estimates for the solutions of
(i)  x^2 – 4x – 2 = 0
 ........................................................... 
(ii)  x^2 – 4x – 6 = 0
 ........................................................... 
(3)
(b)  Use the graph to find estimates for the values of x that satisfy the simultaneous equations
        y = x^2 – 4x – 2
        x + y = 6
 ........................................................... 
(3)
Q8.
 Here is the graph of y = x^2 – 3

Use the graph to find estimates for the solutions to the equation x^2 – 2x – 2 = 0 
You must show how you get your solutions.

 ........................................................... 
 (4)