Quadratic Functions

Quadratic Functions

By Vilochana Veloo

Intercepts

x- intercepts

• The values of x at which the graph crosses on the x-axis

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• To find the x-intercept, let y = 0 in the graph function

  y = ax² + bx + c.​

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Intercepts

y - intercept

• The value of y that the graph crosses on the y - axis

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• ​To find the y-intercept, let x = 0 in the graph function y = ax² + bx + c.

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Turning Point

​Minimum / Maximum Point

• A quadratic graph with a positive x² coefficient has a minimum point (the lowest point on the graph).

• A quadratic graph with a negative x² coefficient has a maximum point (the highest point on the graph).

• ​The line of symmetry passes through the turning point of a quadratic graph.​

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Multiple Choice

What are the x- intercepts of the graph $$y=\left(x-4\right)\left(x+5\right)$$  ?

• $$x=4,\ x=5$$  

• $$x=-5,\ x\ =\ 4$$  

• $$x=-4,\ x\ =\ 5$$  

Multiple Choice

The diagram shows the curve $$y=-\left(x+3\right)\left(x-1\right)$$  .

(i) Find the coordinates of A and of B.

• A (-1, 0), B (3, 0)

• A (1, 0), B (-3, 0)

• A ( -3, 0), B (1, 0)

Multiple Choice

The diagram shows the curve $$y=-\left(x+3\right)\left(x-1\right)$$  .

(ii) Find the coordinates of C.

• C (3, 0)

• C (0, 3)

• C (0, -3)

Multiple Choice

The diagram shows the curve $$y=-\left(x+3\right)\left(x-1\right)$$  .

(iii) The equation of the line of symmetry is $$x=-1$$ . Determine the coordinates of the maximum point of the curve.

• (-1, 4)

• (1, 4)

• (4, -1)

Multiple Choice

In the diagram, the curve $$y=\left(x-4\right)\left(x+2\right)$$  cuts the x-axis at the points A and B, and the y-axis at the point C.

(i) Find the coordinates of A and of B.

• A (-4, 0), B (2, 0)

• A (-2, 0), B (4, 0)

• A (4, 0), B (-2, 0)

Multiple Choice

In the diagram, the curve $$y=\left(x-4\right)\left(x+2\right)$$  cuts the x-axis at the points A and B, and the y-axis at the point C.

(ii) Find the coordinates of C.

• C (0, 8)

• C (0, -8)

• C (-8, 0)

Multiple Choice

In the diagram, the curve $$y=\left(x-4\right)\left(x+2\right)$$  cuts the x-axis at the points A and B, and the y-axis at the point C.

(iii) The point P (-3, k) lies on the curve. Find the value of k.

• -7

• 5

• 7

Multiple Choice

In the diagram, the curve $$y=\left(x-4\right)\left(x+2\right)$$  cuts the x-axis at the points A and B, and the y-axis at the point C.

(iv) Determine the coordinates of the minimum point of the curve.

• (1, -9)

• (-1, 8)

• (1, 8)