GHS Algebra I - Topic 8 Lesson 2: Vertex Form of Quadratic

What is the vertex form of a quadratic function?

• $f\left(x\right)=a\left(x-h\right)^2+k$

• $y=mx+b$

• $f\left(x\right)=a\left|x-h\right|+k$

• $\left(a+b\right)\left(a-b\right)=a^2-b^2$

• $a^2+b^2=c^2$

How can the vertex form of a quadratic function help you sketch the graph of the function? Select all that apply.

• Use $a$ as the slope and $k$ as the y-intercept.

• Plot the vertex at $\left(h,\ k\right)$ .

• Plot a second point 1 unit right or left of the vertex and $a$ units up or down.

• Use $h$ as the x-intercept and $k$ as the y-intercept.

• Use the axis of symmetry $x=h$ to reflect additional points.

How does the graph of $g\left(x\right)=x^2-4$ compare to that of $f\left(x\right)=x^2$ ?

• The graph of $g$ is shifted 4 units up from $f$ .

• The graph of $g$ is shifted 4 units right from $f$ .

• The graph of $g$ is shifted 4 units down from $f$ .

• The graph of $g$ is shifted 4 units left from $f$ .

• The graph of $g$ is flipped and stretched by a factor of 4.

How does the graph of $g\left(x\right)=x^2+3$ compare to that of $f\left(x\right)=x^2$ ?

• The graph of $g$ is shifted 3 units up from $f$ .

• The graph of $g$ is shifted 3 units right from $f$ .

• The graph of $g$ is shifted 3 units down from $f$ .

• The graph of $g$ is shifted 3 units left from $f$ .

• The graph of $g$ is stretched by a factor of 3.

How does the graph of $g\left(x\right)=\left(x-3\right)^2$ compare to that of $f\left(x\right)=x^2$ ?

• The graph of $g$ is shifted 3 units up from $f$ .

• The graph of $g$ is shifted 3 units right from $f$ .

• The graph of $g$ is shifted 3 units down from $f$ .

• The graph of $g$ is shifted 3 units left from $f$ .

• The graph of $g$ is flipped and stretched by a factor of 3.

How does the graph of $g\left(x\right)=\left(x+1\right)^2$ compare to that of $f\left(x\right)=x^2$ ?

• The graph of $g$ is shifted 1 units up from $f$ .

• The graph of $g$ is shifted 1 units right from $f$ .

• The graph of $g$ is shifted 1 units down from $f$ .

• The graph of $g$ is shifted 1 units left from $f$ .

• The graph of $g$ is flipped and shrunk by a factor of 1.

What information do the values of $h$ and $k$ provide about the graph of $f\left(x\right)=\left(x-h\right)^2+k$ ? Select all that apply.

• The x-intercept is $\left(h,\ 0\right)$ .

• The vertex is $\left(h,\ k\right).$  

• The y-intercept is $\left(0,\ k\right).$  

• The slope is $\frac{h}{k}.$  

• The axis of symmetry is $x=h.$  

How does the value of $a$ affect the graph of $f\left(x\right)=a\left(x-h\right)^2+k$ ? Select all that apply.

• If $a$ is positive, the parabola opens up.

• If $a$ is negative, the parabola opens down.

• If $\left|a\right|>1,$ the parabola is stretched vertically.

• The slope is $a.$  

• If $0<\left|a\right|<1,$ the parabola is shrunk vertically.

How does the graph of $f\left(x\right)=-3\left(x-5\right)^2+7$ compare to that of the parent function? Select all that apply.

• The graph of $f$ is shifted right 5 units.

• The graph of $f$ is shifted up 7 units.

• The graph of $f$ has a slope of $-3$ .

• The graph of $f$ is flipped upside down.

• The graph of $f$ is stretched by a factor of 3.

What is the vertex of $f\left(x\right)=-3\left(x-2\right)^2+1$ ?

•  $\left(-2,\ 1\right)$  

•  $x=-11$  

•  $\left(1,\ -2\right)$  

•  $\left(6,\ 0\right)$  

•  $\left(2,\ 1\right)$