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In this lesson, we will learn how to identify features of quadratic equations, such as its vertex, maximum or minimum value, axis of symmetry, domain, and range.

Q1:

Find the coordinates of the vertex of the function π ( π₯ ) = β 7 π₯ + 7 π₯ + 5 2 .

Q2:

Find the coordinates of the vertex of the graph of π ( π₯ ) = π₯ β 6 π₯ β 4 2 . State the value of the function at the vertex and determine whether it is a maximum or minimum value.

Q3:

Find the axis of symmetry of the graph of π ( π₯ ) = 4 π₯ + 4 π₯ β 3 2 .

Q4:

The graph of the quadratic function π intersects the π₯ -axis at the points ( 2 , 0 ) and ( 4 , 0 ) . What is the π₯ -coordinate of the vertex of the graph?

Q5:

The graph of the function π ( π₯ ) = π π₯ + π‘ π₯ + π§ 2 passes through the point ( 0 , 0 ) . Given that the minimum value of the function is β 8 , and the axis of symmetry is the line π₯ = 1 , find the the values of π , π‘ , and π§ .

Q6:

Determine the domain and the range of the function π ( π₯ ) = 4 ( π₯ β 4 ) β 3 2 .

Q7:

Determine the domain and the range of the function π ( π₯ ) = π₯ + 8 π₯ + 2 0 2 .

Q8:

For the function π ( π₯ ) = β 4 π₯ + 5 π₯ + 2 1 2 , answer the following questions.

Find, by factoring, the zeros of the function.

Identify the graph of π .

Write the equation for π , the function that describes the yellow graph.

Write the equation for β , the function that describes the blue graph.

Q9:

For the function π ( π₯ ) = π₯ β 4 π₯ + 3 2 , answer the following questions.

Write the equation for π , the function that describes the blue graph.

Write the equation for β , the function that describes the green graph.

Q10:

For the function π ( π₯ ) = 3 0 π₯ + 9 π₯ β 1 2 2 , answer the following questions.

Q11:

The following statements refer to the function π ( π₯ ) = π π₯ + π π₯ + π ο¨ . Which statement is true?

Q12:

A ball is hurled upward from the top of a building. Its height in feet at time π‘ , in seconds, can be described by the function π» ( π‘ ) = β 1 6 π‘ + 6 4 π‘ + 1 2 0 ο¨ . How many seconds did it take for the ball to reach its maximum height?

Q13:

What are the coordinates of the vertex of the graph of π ( π₯ ) = ( π₯ + 2 2 ) 2 ?

Q14:

Let π be the function in the given table and π ( π₯ ) = ( 2 π₯ + 1 ) β 4 ο¨ .

Which of the following is true?

Q15:

The shown table is that of quadratic function π .

Which of the following has an axis of symmetry closest to π ?

Q16:

Determine the quadratic function π with the following properties:

Q17:

A stone is projected vertically upwards. Its height above the ground β after π‘ seconds is given by Find the maximum height the stone reaches.

Q18:

The function π ( π₯ ) = π β 3 π₯ 2 intersects the π₯ -axis at the point ( 1 , π ) . Find the value of π + 2 π π .

Q19:

An objectβs height in feet, π¦ , is the function π¦ = β π₯ + 9 6 π₯ ο¨ of the horizontal distance traveled, π₯ feet, from where it is projected. What is the maximum height of this motion?

Q20:

Find the coordinates of the vertex of the graph of π ( π₯ ) = π₯ + 4 π₯ + 5 2 . State the value of the function at the vertex and determine whether it is a maximum or minimum value.

Q21:

Find the coordinates of the vertex of the graph of π ( π₯ ) = β π₯ + 2 π₯ + 2 2 . State the value of the function at the vertex and determine whether it is a maximum or minimum value.

Q22:

Find the coordinates of the vertex of the function π ( π₯ ) = π₯ + 8 π₯ β 4 2 .

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