Sketch the graph of $y = |2x + a|$, where $a$ is a positive constant - AQA - A-Level Maths Mechanics - Question 4 - 2018 - Paper 3
Question 4
Sketch the graph of $y = |2x + a|$, where $a$ is a positive constant.
Show clearly where the graph intersects the axes.
Worked Solution & Example Answer:Sketch the graph of $y = |2x + a|$, where $a$ is a positive constant - AQA - A-Level Maths Mechanics - Question 4 - 2018 - Paper 3
Step 1
Draw the V-shape graph
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To sketch the graph of y=∣2x+a∣, we start by recognizing that the absolute value function creates a V-shape. The graph opens upwards and cannot go below the x-axis, indicating that there will be a vertex at the point where 2x+a=0.
Step 2
Intersect the graph with the x-axis
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To determine where the graph intersects the x-axis, we set y=0:
egin{align*} 0 &= |2x + a| \ 2x + a &= 0 \ 2x &= -a \ x &= -\frac{a}{2} \end{align*}
Thus, the graph intersects the x-axis at the point (−2a,0).
Step 3
Intersect the graph with the y-axis
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To find the y-intercept, we set x=0:
y=∣2(0)+a∣=∣a∣=a
Thus, the graph intersects the y-axis at the point (0,a). This concludes the intersection points of the graph with the axes.
