How can you find the coordinates of the turning point of a quadratic graph?

To find the coordinates of the turning point of a quadratic graph, you can either: complete the square differentiate and set the derivative equal to zero to find the x-coordinate

IGCSEMaths A: HigherEdexcelFlashcards

Graphs of Functions (Edexcel IGCSE Maths A)

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FrontTypes of Graphs
Will the vertex of the graph $y = - x^{2} + x + 5$ be a maximum or a minimum point?

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Will the vertex of the graph $y = - x^{2} + x + 5$ be a maximum or a minimum point?
The vertex of the graph $y = - x^{2} + x + 5$ will be a maximum point.
The vertex of a quadratic graph will be a maximum point if the coefficient of $x^{2}$ is negative.
Why does the graph of $y = \frac{1}{x}$ not touch the y-axis?
The graph of $y = \frac{1}{x}$ not touch the y-axis because on the y-axis, $x = 0$ . You can not divide by zero therefore the graph does not have any values on the y-axis.
Where does the graph of $y = 3 (x - 1) (x + 2)$ cross the x-axis?
The graph of $y = 3 (x - 1) (x + 2)$ crosses the x-axis at $(1, 0)$ and $(- 2, 0)$ .
To find these roots, make each factor equal to zero to find the x-coordinate.
How can you find the coordinates of the turning point of a quadratic graph?
To find the coordinates of the turning point of a quadratic graph, you can either:
- complete the square
- differentiate and set the derivative equal to zero to find the x-coordinate
True or False?
The coordinates of the turning point of $y = 4 - {(x - 1)}^{2}$ are $(4, 1)$ .
True or False?
The coordinates of the turning point of $y = 4 - {(x - 1)}^{2}$ are not $(4, 1)$ .
The x-coordinate is the value that makes the squared bracket equal to zero.
The coordinates should be $(1, 4)$ .
True or False?
The solutions to $x^{3} - 4 x = 0$ are the value(s) where the graph $y = x^{3} - 4 x$ crosses the y-axis.
False.
The solutions to $x^{3} - 4 x = 0$ are not the value(s) where the graph $y = x^{3} - 4 x$ crosses the y-axis.
$x^{3} - 4 x = 0$ when $y = 0$ which is the x-axis. Therefore the solutions are the values where the graph crosses the x-axis.
True or False?
The x values of the intersection of the two graphs $y = x + 1$ and $y = x^{2} + 5 x + 4$ are the solutions of $x^{2} + 4 x + 3 = 0$ .
True.
The x values of the intersection of the two graphs $y = x + 1$ and $y = x^{2} + 5 x + 4$ are the solutions of $x^{2} + 4 x + 3 = 0$ .
Set the equations equal to each other and rearrange: $x^{2} + 5 x + 4 = x + 1$ .
The solutions of $x^{3} + x^{2} - 3 = x - 2$ are the x values of the intersection between $y = x^{3} + x^{2} - 3$ and which other graph?
The solutions of $x^{3} + x^{2} - 3 = x - 2$ are the x values of the intersection between $y = x^{3} + x^{2} - 3$ and $y = x - 2$ .
How would you find the y-intercept of a graph using its equation?
To find the y-intercept of a graph, you would substitute $x = 0$ into the equation.
True or False?
The point $(0, 0)$ lies on the graph $y = \sin x$ .
True.
The point $(0, 0)$ lies on the graph $y = \sin x$ .
What is the y-intercept of the graph $y = \cos x$ ?
The y-intercept of the graph $y = \cos x$ is $(0, 1)$ .
What is the minimum y value of the graph $y = \sin x$ ?
The minimum y value of the graph $y = \sin x$ is -1.
True or False?
The graph $y = \cos x$ repeats itself every 180°.
False.
The graph $y = \cos x$ does not repeat itself every 180°.
It repeats itself every 360°.
True or False?
The graph $y = \tan x$ repeats itself every 180°.
True.
The graph $y = \tan x$ repeats itself every 180°.
The graph $y = \sin x$ repeats itself every how many degrees?
The graph $y = \sin x$ repeats itself every 360°.
How would you use a graph of $y = \sin x$ to find the solutions of $\sin x = 0.5$ for $0 ° \leq x \leq 360 °$ ?
To find the solutions of $\sin x = 0.5$ for $0 ° \leq x \leq 360 °$ using the graph $y = \sin x$ :
- calculate one solution using inverse trig $x = \sin^{- 1} (0.5)$
- draw the horizontal line $y = 0.5$
- use the symmetry of the graph to find the other solution*
*For $\sin x$ , you subtract one solution from 180° to find a second solution.
True or False?
The maximum y value on the graph $y = \tan x$ is 1.
False.
The maximum y value on the graph $y = \tan x$ is not 1.
The graph $y = \tan x$ does not have a maximum value.

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