Key Features of Quadratics

Standard Form

100

What is the y-intercept of this quadratic equation?(written as a coordinate point)

y=3x²+2x+5

(0,5)

200

What is the y-intercept of this quadratic equation?(written as a coordinate point)

y+5=4x²+2x-8 

(0,-13)

300

Change this quadratic equation from factored form to standard form?

y=(x-9)(x+2)

y= x²-7x-18

400

Change this quadratic equation from factored form to standard form?

y=4(2x-2)(3x+7)

24x²+32x-56

500

What is the standard form of a quadratic equation and what does c represent?

ax²+bx+c

c represents the y -intercept

Vertex Form

100

What is the vertex of this quadratic equation?

y=4(x+3)²-5

(-3,-5)

200

What is the formula to find the axis of symmetry?

-b/2a

300

What is the vertex of the quadratic function?

y= 3x² -12x+1

(2,-11)

400

What is the vertex of the quadratic function?

y= (x-3)(x+5)

(-1,-16)

500

A researcher found that for the years 2010 to 2016, the equation, y= -0.4(x-3)²+42 models the average gas mileage of new vehicles in Texas, where x is the number of years since 2010 and y is the average gas mileage, in miles per gallon (mpg). Enter a number to show the year when the average gas mileage was the greatest for new vehicles sold in Texas.

2013

Factored Form

100

What are the x-interecpts of this quadratic function? (written as coordinate points)

y= 2(x+2)(x-5)

(5,0) & (-2,0)

200

What are the x-interecpts of this quadratic function? (written as coordinate points)

y= x²-14x+24

(12,0) & (2,0)

300

What are the x-interecpts of this quadratic function? (written as coordinate points)

y= (5x+7)(2x-9)

(-7/5,0) & (9/2,0)

400

A social scientist researches world hunger for the Agriculture Organization. The social scientist measures the undernourished population. The social scientist found the equation, y = 0.2(x + 1) (x - 14)models the relative change as a percentage, y, of the undernourished population x years since 2001.

What are the coordinate points of the x-intercepts?

(-1,0) & (14,0)

500

Fun World Theme Park is building a new roller coaster that goes underground at one point. The equation E(t) = t²- 14t + 33 represents the elevation, E, in feet and the time, t, in seconds, of the roller coaster's path.

How many seconds is the rollercoaster underground for?

8 seconds