Quads: Converting Standard to Vertex form

Transforming Quadratics from Standard Form to Vertex Form

Standard Form of A Quadratic Function

 y=ax²+bx+c

​Graph these quadratics using Desmos Graphing Calculator.

Open Ended

Compare and contrast the two quadratics you graphed using desmos. What do you notice and what do you wonder?

 y=ax²+bx+c

• ​when |a|<1, a is a vertical compression.

• When |a|>1, a is a vertical stretch

• When a is negative, the graph is reflected across the x-axis.

• ​The value of c is where the parabola crosses the y-axis

  (0,c)

Match

Match each graph with its value of a:

is negative

is negative

is negative

• $$\left|a\right|<1$$

• $$a$$ is negative

• $$a$$ is negative

  $$\left|a\right|>1$$

• $$a$$ is negative

  $$\left|a\right|<1$$

• $$\left|a\right|>1$$

Drag and Drop

Determine the y-intercept for the following functions WITHOUT graphing:



$$y=x^2-5$$ ​

Placeholder

$$y=-3x^2-14x+1$$ ​

Placeholder

$$y=\frac{1}{2}x^2-\frac{3}{2}x-\frac{1}{2}$$ ​

Placeholder

$$y=-225x^2+342x$$ ​

Placeholder

Drag these tiles and drop them in the correct blank above

 Using The Standard Form

Evaluating the function at the value of h will give you the corresponding y value, our k value for the vertex.

(h, k) is the vertex of the parabola

Multiple Choice

What is the axis of symmetry equation for the function:

$$y=-3x^2-12x+7$$

• x = 4
• x = 0
• x = -2
• x = 2

Fill in the Blank

What is the h value for the function:

$$y=-3x^2-12x+7$$

(just type the number)

-

Math Response

What is the k value for the function:

$$y=-3x^2-12x+7$$

Type answer here

Correct Answer: 19

Deg^°

Rad

Fill in the Blank

What is the ordered pair for the vertex of the function:

$$y=-3x^2-12x+7$$

(

-

,

)

Math Response

What is the a value for the function:

$$y=-3x^2-12x+7$$

(just type the number)

Type answer here

Correct Answer: -3

Deg^°

Rad

Vertex Form of A Quadratic Function

 y=a(x-h)²+

​Use your knowledge that you just gained to transform the standard form of the quadratic function to the vertex form.

Math Response

What is the vertex form of the function? WITHOUT graphing it.

$$y=-3x^2-12x+7$$

Type answer here

Correct Answer: y=-3\left(x+2\right)^2+19

Deg^°

Rad

Multiple Choice

What is the vertex of the function? WITHOUT graphing it.

$$y=-x^2+4x-9$$

• $$\left(2,\ -13\right)$$

• $$\left(-2,\ \ -21\right)$$

• $$\left(2,\ 3\right)$$

• $$\left(2,\ -5\right)$$

Multiple Choice

What is the vertex form of the equation for the function? WITHOUT graphing it.

$$y=-x^2+4x-9$$

• $$y=-\left(x-2\right)^2-13$$

• $$y=-\left(x+2\right)^2-21$$

• $$y=-\left(x-2\right)^2+3$$

• $$y=-\left(x-2\right)^2-5$$