Quadratic Relationships

solve this quadratic equation by square root. What are the answers. 3x^2+7=55

• 4

• -2

• -4

• 2

solve this quadratic equation using square root . 2x^2 = 12x + 54

• 9

• ( 9, -3 )

• -3

• (-9 , -3 )

The Vertex of a Quadratic relationship (the Maximum amount in relationships that are going down, decreasing...OR Minimum amount in relationships that are going up, increasing) can be determined by?

• Observing the Table of Values for a Quadratic and finding where the measured amounts repeat.

• Observing the graphical presentation and seeing where the relationship "turns around."

• Computing the "time" when it occurs using the Axis Of Symmetry formula , then substituting that time into the expression and evaluating it to determine it's height (measured amount); Using x = -b/(2a)

• All of the processes described could help determine, compute, observe, and/or identify the Vertex of a Quadratic relationship.

The "roots" of a Quadratic relationship are identified as when the relationship measures "0". Often the can be asked as when f(x) = 0. Other descriptions of the roots include?

• The x-intercepts (when the relationship crosses the x-axis).

• The "Zeros" when the relationship measures zero.

• Both of the descriptions are equivalent forms of asking about the "roots".

• Neither of the descriptions are equivalent forms of asking about the "roots".

The y-intercept (initial value) for the Hopeful Launch h(t) can be determined, identified or observed by?

• Observing the "c" coefficient in it's equation presented in Standard Form c = 24.

• Investigating the Table of Values and noticing that at time 0 (t = 0 or h(0)) the relationship equal 24.

• Inspecting the graph and identifying the height at time zero, or along the y-axis, and seeing that it crosses the y-axis at a measured height of 24 feet.

• All of the described processes are possible methods of determining the y-intercept (initial value) of a function.

Technically, the Vertex of h(t) is?

• h(2) = 72 or (2, 72)

• h(3) = 72 or (3, 72)

• h(2.5) = 74 or (2.5, 74)

• All of the above

The Vertex of the Quadratic relationship g(t) "Go Far" (the Maximum height as it sores through the air and eventually goes down- decreases) can be determined by?

• Observing the graph and identifying it's highest point

• Investigating it's table of values and finding where the repeated measured amounts occur in the g(x) column.

• Computing the "time" when it occurs using the axis Of Symmetry formula, then substituting that time into the expression and evaluating it to determine it's height (measured amount); Using x = -b /(2a)

• All of the above

To determine the actual "measured amount" at the time the vertex occurs you should?

• Evaluate the function at the time of the axis of symmetry. Substitute the "x" value of the time of the axis of symmetry into the original relationship and compute it's value at that time.

• Determine the value of the relationship for g(0) to compute the y-intercept.

• Both processes are appropriate methods to compute the value of the vertex

• Neither process properly describes how to compute the value of the vertex Algebraically.

The cool thing about Vertex Form of a Quadratic relationship is that?

• You can see the y-intercept in the formula, the value at time zero.

• You can observe the Vertex right in the form itself without any further manipulations or investigations! (BUT you cannot see the y-intercept, value at time zero)

• Both explanations/observations are true

• Neither explanation/observation is true

A Quadratic and Linear System could possibly have?

• One solution, Two Solutions, or No Solution

• One Solutions, No Solution, or an Infinite Number of solutions

• One or two Solutions

• None of the descriptions of Solutions are correct