IB myp 4-5 MATHEMATICS – Practice Questions- All Topics
Topic :Algebra-Factorizing Quadratic Expressions
Topic :Algebra- Weightage : 21 %
All Questions for Topic : Fcatorizing Quadratic Expressions,Solving Quadratic Expressions,Changing the subject of the equation
Question (6 Marks)
The following diagram shows part of the graph of a quadratic function $f(x)=x^2-8 x+12$
Question (a) : 1 marks
Write down the coordinates of point $\rm C$.
▶️Answer/Explanation
Ans:
To find the coordinates of point C on the y-axis, we need to determine the x-coordinate of C and then substitute it into the equation of the quadratic function to find the corresponding y-coordinate.
Since point C is on the y-axis, its x-coordinate is $0.$
Now, let’s substitute $x = 0$ into the equation of the quadratic function to find the y-coordinate:
$f(x) = x^2 – 8x + 12$
$f(0) = 0^2 – 8(0) + 12$
$f(0) = 0 – 0 + 12$
$f(0) = 12$
Therefore, the coordinates of point C are $(0, 12).$
Question (b) : 4 marks
Find the coordinates of points $\mathrm{A}$ and $\mathrm{B}$.
▶️Answer/Explanation
Ans:
To find the coordinates of points A and B on the x-axis, we need to determine the y-coordinate of each point. Since points A and B lie on the x-axis, their y-coordinates are both zero.
Let’s first find the x-coordinate of point A. To do this, we set the equation of the quadratic function equal to zero and solve for x:
$x^2 – 8x + 12 = 0$
We can factor this quadratic equation as follows:
$(x – 2)(x – 6) = 0$
Setting each factor equal to zero:
$x – 2 = 0 \quad \text{or} \quad x – 6 = 0$
Solving these equations:
$x = 2 \quad \text{or} \quad x = 6$
Therefore, the x-coordinate of point A is 2.
Similarly, we can find the x-coordinate of point B:
$x = 6$
So, the coordinates of point A are (2, 0) and the coordinates of point B are (6, 0).