Writing Quadratic Functions

Match

Match the following quadratic functions with their vertex.

• $$x^2+8x-2$$

• $$x^2-2x-3$$

• $$-2x^2-16x+5$$

• $$-3x^2-12x+3$$

• $$4x^2+24x+32$$

(-4, -18)

(1, -4)

(-4, 37)

(-2, 15)

(-3, -4)

• (-4, -18)

• (1, -4)

• (-4, 37)

• (-2, 15)

• (-3, -4)

Labelling

Label the key features of the parabola.

Drag labels to their correct position on the image

Axis of symmetry

y-intercept

x-intercepts(roots, zeros or solutions)

Vertex

Multiple Choice

What is the vertex for
$$y=4(x-2)^2+3$$

• (-2, 3)
• (2,-3)
• (4,3)
• (2,3)

Multiple Choice

What is the vertex of the parabola: $$y=2(x-3)^2+4$$

• (3,4)
• (-3,4)
• (3, -4)
• (-3,-4)

Multiple Choice

Does the parabola
$$y=4(x-2)^2+3$$
open up or down?

• up
• down

Multiple Choice

Identify the vertex and whether the graph opens up or down.

• (5, 2); opens up
• (5, 2); opens down
• (-5, 2); opens up
• (-5, 2); opens down

Multiple Choice

What is the equation of this graph?

• $$y=(x-5)^2+1$$

• $$y=(x-1)^2-5$$

• $$y=(x+1)^2-5$$

• $$y=(x+5)^2+1$$

Multiple Choice

Which equation is graphed above?

• $$y=-\left(x-1\right)^2+4$$

• $$y=\left(x-1\right)^2+4$$

• $$y=-\left(x-4\right)^2+1$$

• $$y=\left(x-4\right)^2+1$$

Math Response

What is the equation for the graph? (written in vertex form)

Type answer here

Correct Answer: y=2\left(x+4\right)^2-3

Deg^°

Rad

Math Response

What is the equation for the graph? (written in vertex form)

Type answer here

Correct Answer: y=-3\left(x-5\right)^2+3

Deg^°

Rad

Math Response

What is the equation for the graph? (written in vertex form)

Type answer here

Correct Answer: y=-\frac{3}{4}\left(x-2\right)^2+5

Deg^°

Rad

Multiple Choice

What is the quadratic equation of a parabola with a vertex of (-4, 1) and goes through the point (-8, 14)?

• $$f\left(x\right)=\frac{1}{2}\left(x+4\right)^2+6$$

• $$f\left(x\right)=2\left(x-4\right)^2-1$$

• $$f\left(x\right)=\frac{3}{4}\left(x+6\right)^2+4$$

• $$f\left(x\right)=4\left(x-2\right)^2+6$$

Math Response

Use the table to write the quadratic function, in vertex form.

Type answer here

Correct Answer: y=4\left(x+2\right)^2+7

Deg^°

Rad

Multiple Choice

Given the table, determine the equation of the function.

• y = 2(x-2) + 4
• y = -1(x-2)² + 4
• y = 1(x-1)² - 4
• y = 2(x-1)² - 4

Multiple Choice

Given the table, determine the equation of the function.

• $$y=(x+3)^2+8$$

• $$y=-(x+3)^2+8$$

• $$y=(x-3)^2+8$$

• $$y=-(x-3)^2-8$$

Multiple Choice

Convert
  $$y=2(x-2)^2+9$$
to standard form.

• $$y=2x^2+8x+9$$

• $$y=2x^2-8x-4$$

• $$y=2x^2-8x+17$$

• $$y=2x^2-8x+8$$

Math Response

Convert the quadratic function $$y=2\left(x-3\right)^2+4$$ to standard form.

(no spaces and use the letters x & y for the variables)

Type answer here

Correct Answer: y=2x^2-12x+22

Deg^°

Rad

Math Response

Convert the quadratic function $$y=2\left(x-4\right)^2+3$$ to standard form.

(no spaces and use the letters x & y for the variables)

Type answer here

Correct Answer: y=2x^2-16x+35

Deg^°

Rad

Math Response

Convert the vertex form function below to standard form.

$$y=\frac{1}{2}\left(x-6\right)^2-10$$

(No spaces and use x and y for the variables)

Type answer here

Correct Answer: y=\frac{1}{2}x^2-6x+8

Deg^°

Rad