B-Man Methods of Solving Quadraticts

Solving Quadratics ~ Methods

Solving Quadratics ~ Examples

Solving Quadratics ~ Process for Using the Quadratic Formula

Solving Quadratics ~ Example

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Given the Quadratic Equation: 2x² + 5x + 3 = 0.

Identify the values to use in the Quadratic Formula.

a = ​

Select answer

^{b =} ​

Select answer

c = ​

Select answer

Dropdown

Given the Quadratic Equation: -16t² + 48t + 8 = 0.

Identify the values to use in the Quadratic Formula.

a = ​ ​ ​

Select answer

^{b =} ​ ​ ​

Select answer

c = ​ ​ ​

Select answer

Dropdown

Given the Quadratic Equation: -x² - 7x - 13 = 0.

Identify the values to use in the Quadratic Formula.

a = ​ ​

Select answer

^{b =} ​ ​

Select answer

c = ​ ​

Select answer

Multiple Choice

Which shows proper substitution into the Quadratic Formula to solve the equation:

$$x^2-7x+6=0$$

• $$x=\frac{-7\pm\sqrt[]{\left(-7\right)^2-4\left(1\right)\left(6\right)}}{2\left(1\right)}$$

• $$x=\frac{-\left(-7\right)\pm\sqrt[]{\left(-7\right)^2-4\left(1\right)\left(6\right)}}{2\left(1\right)}$$

• $$x=\frac{-\left(-7\right)\pm\sqrt[]{-7^2-4\left(1\right)\left(6\right)}}{2\left(1\right)}$$

• $$x=\frac{-7\pm\sqrt[]{-7^2-4\left(1\right)\left(6\right)}}{2\left(1\right)}$$

Multiple Choice

Use the Quadratic Formula to solve this equation. Simplify answers.

$$2x^2+x-15=0$$

• $$x=\frac{-1\pm\sqrt[]{1^2-4\left(2\right)\left(-15\right)}}{2\cdot2}$$ $$x=\frac{-1\pm\sqrt[]{121}}{4}$$

  $$x=\frac{-1\pm11}{4}$$

  $$x=\frac{-1-11}{4}$$

  or

  $$x=\frac{-1+11}{4}$$

  $$x=-\frac{12}{4}\ or\ x=\frac{10}{4}$$

  $$x=-3\ \ or\ \ x=2.5$$

• $$x=\frac{-1\pm\sqrt[]{1^2-4\left(2\right)\left(15\right)}}{2\cdot2}$$

  $$x=\frac{-1\pm\sqrt[]{-119}}{4}$$

  No real solution since the square root of -119 is NOT a real number.

• $$x=\frac{-1\pm\sqrt[]{1^2-4\left(2\right)\left(-15\right)}}{2\cdot2}$$ $$x=\frac{-1\pm\sqrt[]{121}}{4}$$

  $$x=\frac{-1\pm11}{4}$$

  $$x=\frac{-1-11}{4}$$

  or

  $$x=\frac{-1+11}{4}$$

  $$x=-\frac{12}{4}\ or\ x=\frac{10}{4}$$

  $$x=3\ \ or\ \ x=-2.5$$

• $$x=\frac{-1\pm\sqrt[]{1^2-4\left(2\right)\left(-15\right)}}{2\cdot2}$$ $$x=\frac{-1\pm\sqrt[]{121}}{4}$$

  $$x=\frac{-1\pm11}{4}$$

  $$x=\frac{-1-11}{4}$$

  or

  $$x=\frac{-1+11}{4}$$

  $$x=\frac{12}{4}\ or\ x=\frac{10}{4}$$

  $$x=3\ \ or\ \ x=2.5$$

Match

Match the technique used to solve this equation with the solution given.

$$7x^2-252=0$$

ALL give correct solutions to the equation.

• $$7x^2=252$$

  $$x^2=36$$

  $$x=\pm6$$

• $$7\left(x^2-36\right)=0$$

  $$7\left(x+6\right)\left(x-6\right)=0$$

  $$x=-6\ \ or\ \ \ x=6$$

• $$x=\frac{-0\pm\sqrt[]{0^2-4\cdot7\left(-252\right)}}{2\cdot7}$$ $$x=\frac{\pm\sqrt[]{70546}}{14}$$

  $$x=\pm6$$

Using Square Roots

Factoring and Using Zero Product Propert

Using the Quadratic Formula

Graphing and Using the Zeros

• Using Square Roots

• Factoring and Using Zero Product Propert

• Using the Quadratic Formula

• Graphing and Using the Zeros

Categorize

Options (12)

$$x^2=49$$  

$$x^2+5x+6=0$$  

$$x^2+4x-7=0$$  

$$6x^2+40=64$$  

$$-3m^2+21=-21$$  

$$4x^2+12x+5=0$$  

$$-16t^2+640t=0$$  

$$3x^2-8x-9=0$$  

$$11x^2+13x-15=0$$  

Organize these options into the method that would be MOST convenient to solve the quadratic equation.

Using Square Root

Factoring and Z.P.P.

Using Quad Formula

Graphign & x-Int.

​Use this link to investigate projectile motion in Desmos:
https://www.desmos.com/calculator/af50y6a0hd

Dropdown

A baseball is launched straight upward, from a height of 6.4 ft. with an initial velocity of 48 ft./sec. Given the vertical motion function: h(t) = -16t² + v₀t + h₀ , select the correct substitution into the formula.

​

Select answer

Reorder

A baseball is launched straight upward, from a height of 6.4 ft. with an initial velocity of 48 ft./sec. Given the vertical motion function: h(t) = -16t² + v₀t+ h₀ , order the steps needed to find how long the ball is in the air.

• $$0=-16t^2+48t+6.4$$ Set h(t) = 0 

• $$t=\frac{-48\pm\sqrt[]{48^2-4\left(-16\right)\left(6.4\right)}}{2\left(-16\right)}$$ Substitute into Q.F.

• $$t=\frac{-48\pm\sqrt[]{2713.6}}{-32}$$ Simplify.

• $$t=\frac{-48-\sqrt[]{2713.6}}{-32}$$ or

  $$t=\frac{-48+\sqrt[]{2713.6}}{-32}$$ Separately evaluate each root on calc.

• $$t\approx-0.13$$

  or

  $$t\approx3.13$$

  Choose the positive value: The ball will be in the air about 3.13 sec.

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Enjoy the video at the right!


What projectile motion do you see in this video?

How could we determine the launch velocity of the bob?

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For your entertainment:

Open Ended

Consider the bob in the "strong man" bell ringer video on the previous slide. Describe how the initial velocity of the bob could be determined in each of the attempts. State what information would be needed to solve for the initial velocity in the projectile motion formula:

$$h\left(t\right)=-16t^2+v_0t+h_0$$