(Alg.2) 4.1 Graphing Quadratics Functions.

Does the equation open up or down? y = -3x² + 7x - 2

• up

• down

• Neither; it opens to the right.

• Neither; it opens to the left.

Answer explanation

The equation Y = -3x² + 7x - 2 is a quadratic function. The coefficient of x² is -3, which is negative. This indicates that the parabola opens downwards. Therefore, the correct answer is 'down'.

Tags

CCSS.HSF-IF.C.7A

What is the name of this form: y = ax² + bx + c

• vertex form

• standard form

• factored form

• zero form

Answer explanation

The equation y = ax² + bx + c is in standard form, which represents a quadratic function. The other forms, such as vertex form and factored form, have different structures and purposes.

What is the maximum/minimum of a parabola called?

• vertex

• point

• top

• bottom

Answer explanation

The maximum or minimum point of a parabola is called the vertex. It represents the highest point (maximum) or the lowest point (minimum) of the parabola, depending on its orientation.

What do we call the graph of a quadratic function?

• parabola

• linear

• cubic

• sinusoidal

Answer explanation

The graph of a quadratic function is called a parabola. This U-shaped curve can open upwards or downwards, distinguishing it from linear (straight line), cubic (S-shaped), and sinusoidal (wave-like) graphs.

Tags

CCSS.HSF-IF.C.7A

What is the vertex of this parabola?

• (−1, 3)

• (−3, 11)

• (−2, 5)

• (0, 5)

Answer explanation

To find the vertex of the parabola, we can use the vertex formula or complete the square. The correct vertex is (−1, 3), which represents the highest or lowest point of the parabola, depending on its orientation.

What is the formula above primarily used for?

• Finding the axis of symmetry from standard form

• Finding the vertex from standard form

• Finding the vertex from vertex form

• Finding the vertex from standard form

Answer explanation

The formula is primarily used for finding the axis of symmetry from standard form. This is determined using the formula x = -b/(2a), which directly relates to the coefficients in the standard form of a quadratic equation.

How do you know if a parabola has a minimum?

• When ‘a’ is positive there is a minimum

• When ‘a’ is negative there is a minimum

• When all the numbers in the equation are negative there is a minimum

• When all the numbers in the equation are positive there is a minimum

Answer explanation

A parabola opens upwards and has a minimum point when the coefficient 'a' in the quadratic equation y = ax^2 + bx + c is positive. This indicates that the arms of the parabola extend upwards.

Tags

CCSS.HSF-IF.C.7A

What is the equation for axis of symmetry?

• y = 3

• x = 3

• x = 5

• x = 1

Answer explanation

The axis of symmetry for a parabola in the form y = ax^2 + bx + c is given by the formula x = -b/(2a). If the vertex is at (3, y), then the axis of symmetry is x = 3, making this the correct choice.

Tags

CCSS.HSF-IF.C.7A

How can you tell whether a parabola opens up or opens down by looking at the equation?

• The vertex tells you the direction of the opening

• The value of "a" tells you the direction of the opening.

• All parabolas open upward

• All parabolas open downward

Answer explanation

The value of 'a' in the quadratic equation y = ax^2 + bx + c determines the direction of the parabola's opening. If 'a' is positive, the parabola opens upward; if 'a' is negative, it opens downward.

Tags

CCSS.HSF-IF.C.7A

What is the graph of the equation f(x) = -2x² + 12x - 20?

• A
• B
• C
• D

Tags

CCSS.HSF-IF.C.7A