Question
© Draw the graph of the function
in the domain
, where
,
on the co-ordinate grid opposite. Show your working out.
,
on the co-ordinate grid opposite. Show your working out.
,
Ask by Delgado Lyons. in Ireland
Jan 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
To graph the function
between
and
, follow these steps:
-
Find the Vertex and Axis of Symmetry:
- Vertex at
- Axis of symmetry at
- Vertex at
-
Determine Intercepts:
- Y-intercept at
- X-intercepts at
and
- Y-intercept at
-
Plot Additional Points:
-
-
Sketch the Parabola:
- Draw a smooth, upward-opening curve through the plotted points, ensuring symmetry around the axis
.
- Draw a smooth, upward-opening curve through the plotted points, ensuring symmetry around the axis
The graph shows a parabola with the vertex at
, y-intercept at
, and x-intercepts at
and
within the domain
.
Solution

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Mind Expander
To graph the function
for the domain
, start by calculating some key points:
-
Calculate the function values:
-
-
Plot the points:
- The points you will plot are:
-
- The points you will plot are:
-
Sketch the quadratic graph:
- Connect the points smoothly, keeping in mind that this is a parabolic curve that opens upwards because the coefficient of
is positive.
- Connect the points smoothly, keeping in mind that this is a parabolic curve that opens upwards because the coefficient of
Now, you should see a U-shaped graph that dips down around the vertex between
and
, and rises back up towards
. The vertex can also be calculated using the vertex formula
, giving
which helps in understanding the graph shape further.
When graphing, be sure to label your axes and include the plotted points! Happy graphing!