Quadratic Functions and Zeros

B-Man Evaluating Functions, Parabolas, Vertices & Zeros

Parabolas: Quadratic Functions Describing The Universe's Natural Arches!

Functions as Equations & Graphs ~

​Your Turn! Evaluate the functions on the next few slides.

1. Substitute the INPUT (domain) value in place of x (or whatever the independent variable is) everywhere it appears in the function.
2. Use Order of Operations to simpilfy.
3. State the final relationship.

Best wishes! Stay focused and concentrate!

Multiple Choice

Given $$h\left(t\right)=-16t^2+128t$$ . Evaluate $$h\left(3\right)$$

• $$h\left(3\right)=-16\cdot3^2+128\cdot3$$ $$h\left(3\right)=240\ ft.$$

• $$h\left(3\right)=-16\cdot3^2+128\cdot3$$ $$h\left(3\right)=1008\ ft.$$

• $$h\left(3\right)=-16\cdot3^2+128\cdot3$$ $$h\left(3\right)=6\ ft.$$

• $$h\left(3\right)=-16\cdot3^2+128\cdot3$$ $$h\left(3\right)=\ 2688\ ft.$$

Multiple Choice

Given $$f\left(x\right)=5x^2-3x+8$$ . Evaluate $$f\left(2\right)$$

• $$f\left(2\right)=5\left(2\right)^2-3\cdot2+8$$ $$f\left(2\right)=6$$

• $$f\left(2\right)=5\left(2\right)^2-3\cdot2+8$$ $$f\left(2\right)=22$$

• $$f\left(2\right)=5\left(2\right)^2-3\cdot2+8$$ $$f\left(2\right)=102$$

• $$f\left(2\right)=5\left(2\right)^2-3\cdot2+8$$ $$f\left(2\right)=86$$

Match

Given the function.

Match the function output value (range value) for the given input (domain value).

• $$f\left(x\right)=-3x^2+7x$$

• $$f\left(x\right)=5x^2-2x$$

• $$f\left(x\right)=4x^2+6x$$

• $$f\left(x\right)=6x^2-x$$

• $$f\left(t\right)=-14t^2+28t$$

• $$f\left(4\right)=-20$$

• $$f\left(2\right)=16$$

• $$f\left(7\right)=238$$

• $$f\left(\frac{1}{6}\right)=0$$

• $$f\left(2\right)=0$$

Zeros of a Parabola (Quadratic Function)

Process to Find the
Zeros of a Quadratic Function

Examples of Finding the Zeros of a Quadratic Function

Dropdown

What are the zeros of the function: ​ f(x) = -4x² + 24x

​ ​ ​

Select answer

Match

Match the function with its zeros.

• $$f\left(x\right)=\left(x+2\right)\left(x-8\right)$$

• $$f\left(x\right)=17x\left(5x-4\right)$$

• $$g\left(x\right)=x^2-5x+4$$

• $$h\left(t\right)=-16t^2+64t$$

• $$w\left(x\right)=2x^2+x-3$$

• $$x=-2,\ x=8$$

• $$x=0,\ x=\frac{4}{5}$$

• $$x=1,\ x=4$$

• $$t=0,\ t=2$$

• $$x=-1.5,\ x=1$$

Graphs and Zeros

​Your Turn! Identify either the zeros or the x-intercepts of the functions on the next few slides.

REMEMBER! Zeros are ONLY the x-coordinates of the x-intercepts.

Identify zeros: x = -2 and x = 2

Related x-intercepts: (-2, 0) and (2, 0)


Best wishes! Stay focused and concentrate!

Multiple Choice

State the zeros of the given function shown in the graph.

• $$\left(-50,\ 0\right)$$

• $$x=-50$$

• $$\left(-5,\ 0\right),\ \left(5,\ 0\right)$$

• $$x=-5,\ \ x=5$$

Multiple Choice

The x-intercepts of the graph shown here are:

Be sure to select proper form for x-intercepts.

• $$\left(0,0\right)\ and\ \left(2.2,0\right)$$

• $$x=0\ and\ x=2.2$$

• $$\left(0,0\right)\ and\ \left(2,0\right)$$

• $$\left(0,0\right)\ and\ \left(0,2.2\right)$$

Match

Match the following graphs of quadratic functions with their zeros.

• $$f\left(x\right)=-3x^2+15x$$

• $$f\left(x\right)=x^2-9x+8$$

• $$f\left(x\right)=\left(x-3\right)\left(x+8\right)$$

• $$f\left(x\right)=\left(2x+5\right)\left(3x-21\right)$$