Quadratics Properties

Poll

How much do you remember about Quadratics from Algebra 1 last year?

• 1 (None)

• 2 (Some)

• 3 (Lots!)

Multiple Choice

$$g\left(x\right)=-\left(x+1\right)^2+3$$ is a "transformed function" from the parent function $$f\left(x\right)=x^2$$ and has an x-axis reflection. Which function below also has an x-axis reflection?

• $$h\left(x\right)=-x^2$$  

• $$h\left(x\right)=\left(x+1\right)^2$$  

• $$h\left(x\right)=x^2+3$$  

Multiple Choice

$$g\left(x\right)=4\left(x+1\right)^2+3$$ is a "transformed function" from the parent function $$f\left(x\right)=x^2$$ and has a shift up. Which function below also has a shift up?

• $$h\left(x\right)=4x^2$$  

• $$h\left(x\right)=\left(x+1\right)^2$$  

• $$h\left(x\right)=x^2+3$$  

Multiple Choice

$$g\left(x\right)=4\left(x+1\right)^2+3$$ is a "transformed function" from the parent function $$f\left(x\right)=x^2$$ and has a shift left. Which function below also has a shift left?

• $$h\left(x\right)=4x^2$$  

• $$h\left(x\right)=\left(x+1\right)^2$$  

• $$h\left(x\right)=x^2+3$$  

Multiple Choice

Does this parabola have a maximum or minimum value at y=k?

• Maximum

• Minimum

Multiple Choice

What is the vertex of the following quadratic? (Gridlines are 1 unit)

• (3,-8)

• (-3,8)

• (3,8)

• (-3,-8)

Multiple Choice

What is the vertex of the following quadratic equation? $$f\left(x\right)=2\left(x-1\right)^2+5$$  

• (-1, 5)

• (1, 5)

• (-1, -5)

• (1, -5)

Multiple Choice

What is the axis of symmetry of the following quadratic? (Gridlines are 1 unit)

• x=3

• y=3

• x=-8

• y=8

Multiple Choice

What is the axis of symmetry of the following quadratic? $$y=2\left(x-5\right)^2+1$$  

• x=2

• x=-5

• x=5

• y=1

• y=-1

Multiple Choice

What is the extrema of the following quadratic? (Gridlines are 1 unit)

• Minimum at y=-8

• Minimum at x=-8

• Maximum at y=-8

• Maximum at x=-8

Multiple Choice

What is the domain of the following quadratic?

• All real numbers

• $$x\le3$$  

• $$x\ge3$$  

Multiple Choice

What is the range of the following quadratic?

• $$y\ge-8$$  

• $$x\le3$$  

• $$x\ge3$$  

• $$y\le-8$$  

Multiple Choice

The equation of a quadratic in standard form is $$y=2x^2-5x+3$$ . Identify a, b, and c.

• a=2, b=-5, c=3

• a=2, b=5, c=3

• a=-5, b=2, c=3

• a=2, b=-5, c=-3

Multiple Choice

The standard form of a quadratic is $$y=x^2+4x+3$$  . What is the vertex of the quadratic? (Use $$\frac{-b}{2a}$$  for h and substitute that value into the equation to find k.)

• (h, k) = (-2, 15)

• (h, k) = (2, 15)

• (h, k) = (-2, -1)

• (h, k) = (2, -15)

Multiple Choice

The standard form of a quadratic is $$y=x^2+4x+3$$ . Using $$\frac{-b}{2a}$$  to find h and substituting that value into the equation to find k, the vertex is found to be $$\left(-2,\ -1\right)$$ . What is the vertex form of this quadratic?

• $$y=\left(x+2\right)^2-1$$  

• $$y=\left(x-2\right)^2-1$$  

• $$y=\left(x+2\right)^2+1$$  

• $$y=\left(x-2\right)^2+1$$  

Poll

How confident do you feel about what we learned today?

• 1 (not confident at all)

• 2 (somewhat confident)

• 3 (very confident!)