Algebra 1: Quadratic Functions; standard form

Tempestt graphs a function that has a maximum located at (-4, 2). Which could be her graph?

c

What is the y-intercept of the graph of the function f(x) = x2 + 3x + 5?

(0,5)

What is the x-intercept of the graph of the function f(x) = x2 − 16x + 64?

(8, 0)

Which must be true of a quadratic function whose vertex is the same as its y-intercept?

The axis of symmetry for the function is x = 0.

The a value of a function in the form f(x) = ax2 + bx + c is negative. Which statement must be true?

The vertex is a maximum.

Analyze the graph of a cannonball launched from the ground with an initial velocity of 144 feet per second. The cannonball reached its maximum height after 4.5 seconds. What was the maximum height the cannonball reached?

324 feet

A projectile with an initial velocity of 48 feet per second is launched from a building 190 feet tall. The path of the projectile is modeled using the equation h(t) = -16t2 + 48t + 190.

226 feet

Over which interval is the graph of f(x) = -x2 + 3x + 8 increasing?

(-∞,1.5)

The axis of symmetry for the function f(x) = −x2 − 10x + 16 is x = −5. What are the coordinates of the vertex of the graph?

(−5, 41)

The axis of symmetry for the graph of the function f(x)=3x2+bx+4 is x=3/2 What is the value of b?

-9

Which statements about the graph of the function f(x) = -x2 - 4x + 2 are true? Select three options.

-The range is {y|y ≤ 6}. -The function is increasing over the interval (-∞ , -2). -The function has a positive y-intercept.

A projectile with an initial velocity of 48 feet per second is launched from a building 190 feet tall. The path of the projectile is modeled using the equation h(t) = -16t2 + 48t + 190. Approximately when will the projectile hit the ground?

5.3 seconds

For all functions of the form f(x) = ax2 + bx + c, which is true when b = 0?

The y-intercept will always be the vertex.

projectile graph

parabola graph

f(x)= -x²-2x-1

vertex: maximum value The function is increasing when x<-1 The function is decreasing when x>-1 domain: all real numbers range: all real numbers less than or equal to zero

The graph of which function has an axis of symmetry at x = 3?

d f(x)=x2-6x-1

He concluded that a heavier object dropped from the same height as a lighter object will land ________________________ .

at about the same time as the lighter object

While teaching at the University of Pisa in 1589, Galileo tested Aristotle's laws of falling objects by dropping large metal projectiles off the _______________.

leaning tower of pisa