Transformations of Quadratic Functions

What is the parent function of a quadratic equation?

• f(x)=x

• f(x)=x²

• f(x)=ax²+bx+c

• f(x)=a(x-h)²+k

Answer explanation

The parent function of a quadratic equation is f(x)=x², which represents the simplest form of a quadratic function. Other options represent variations or transformations of this basic quadratic function.

What is the standard form of a quadratic equation?

• f(x)=x

• f(x)=x²

• f(x)=ax²+bx+c

• f(x)=a(x-h)²+k

Answer explanation

The standard form of a quadratic equation is f(x)=ax²+bx+c, where a, b, and c are constants. This form allows for easy identification of the coefficients and the shape of the parabola.

What is the vertex form of a quadratic equation?

• f(x)=x

• f(x)=x²

• f(x)=ax²+bx+c

• f(x)=a(x-h)²+k

Answer explanation

The vertex form of a quadratic equation is f(x)=a(x-h)²+k, where (h,k) is the vertex of the parabola. This form highlights the vertex and is useful for graphing, unlike the standard form ax²+bx+c.

What is the axis of symmetry for this function: (x+4)²-5

• x= 4

• x=-4

• x= 5

• x= -5

Answer explanation

The function (x+4)²-5 is in vertex form, where the axis of symmetry is given by x = -h. Here, h = -4, so the axis of symmetry is x = -4. Thus, the correct answer is x = -4.

What is the vertex of this function: (x+4)²-5

• (4,5)

• (-4,5)

• (4, -5)

• (-4, -5)

Answer explanation

The function (x+4)²-5 is in vertex form y=a(x-h)²+k, where (h,k) is the vertex. Here, h=-4 and k=-5, so the vertex is (-4, -5). Thus, the correct answer is (-4, -5).

Which of these shows a parent function of a quadratic equation moved 5 units to the right?

• f(x)=(x-5)²

• f(x)=(x+5)²

• f(x)=x²-5

• f(x)=x²+5

Answer explanation

The parent function of a quadratic equation is f(x) = x^2. Moving it 5 units to the right involves replacing x with (x-5), resulting in f(x) = (x-5)^2. Thus, the correct choice is f(x)=(x-5)^2.

Which of these shows a parent function of a quadratic equation moved 1 unit down?

• f(x)=(x-1)²

• f(x)=(x+1)²

• f(x)=x²+1

• f(x)=x²-1

Answer explanation

The parent function of a quadratic equation is f(x)=x². Moving it 1 unit down results in f(x)=x²-1, which is the correct choice. The other options either shift horizontally or move up.

What do we call the highest or lowest point of a quadratic?

• parabola

• vertex

• graph

• point

Answer explanation

The highest or lowest point of a quadratic function is called the vertex. It represents the maximum or minimum value of the function, distinguishing it from other terms like parabola, graph, or point.

Tags

CCSS.HSF-IF.C.7A

What is the vertex of the following equation?
y=5(x-3)²+5

• (3,5)

• (-3,5)

• (3, -5)

• (-3,-5)

Answer explanation

The equation y=5(x-3)²+5 is in vertex form y=a(x-h)²+k, where (h,k) is the vertex. Here, h=3 and k=5, so the vertex is (3,5). Thus, the correct answer is (3,5).

Describe the transformations of f(x) when compared to the parent function.
f(x)=x²+5

• horizontal shift right 5 units

• horizontal shift left 5 units

• vertical shift up 5 units

• vertical shift down 5 units

Answer explanation

The function f(x) = x² + 5 is derived from the parent function f(x) = x² by adding 5. This results in a vertical shift up 5 units, moving the entire graph upwards without changing its shape.