GRAPHING QUADRATIC FUNCTIONS
This is the shape of the graph of a quadratic function.
✅ Answer: What is a parabola?
In y=(x−5)2
the graph shifts ___ units right.
✅ Answer: What is 5?
The solutions of a quadratic equation are also called the ______.
✅ Answer: What are x-intercepts or zeros?
Factor x2+6x+9
✅ Answer: What is (x+3)2?
What is the vertex of: y=(x+1)2−5
✅ Answer: What is (−1,−5)
The quadratic function y=x2 opens in which direction?
✅ Answer: What is upward?
In
y=(x+2)2
the graph shifts ___ units left.
✅ Answer: What is 2?
Solve by graphing: x2−9=0
✅ Answer: What are x=−3 and x=3?
Factor:
x2−25
✅ Answer: What is (x+5)(x−5)
Solve x2=49
✅ Answer: What are x=7 and x=−7?
Find the vertex of:
y=(x−3)2 + 2
✅ Answer: What is (3,2)
Describe the transformation:
y=x2−7
✅ Answer: What is shifted 7 units down?
How many solutions does a parabola have if it never touches the x-axis ?
✅ Answer: What is 0?
Determine whether the quadratic expression is factorable over the integers: x2+5x+7
✅ Answer: What is not factorable over the integers?
Is the following expression factorable? Explain.
x2+2x+8
✅ Answer: What is not factorable over the integers?
Identify the axis of symmetry: y=(x+4)2−1
✅ Answer: What is x=−4
Describe the transformation:
y=−x2
✅ Answer: What is reflected across the x-axis?
How many solutions does a parabola have if it touches the x-axis once?
✅ Answer: What is 1?
Determine whether the expression is a perfect square trinomial
x2+10x+25
✅ Answer: What is yes, it is a perfect square trinomial?
Explanation:x2+10x+25=(x+5)2
Identify the factoring pattern: x2−14x+49
✅ Answer: What is a perfect square trinomial?
Factored Form:
(x−7)2
Determine whether the parabola opens up or down: y=−2x2+5
✅ Answer: What is downward?
Describe all transformations:
y=−2(x−3)2+4
✅ Answer:
Solve:
x2−4x+3=0
✅ Answer: What are x=1x=1x=1 and x=3x=3x=3?
Solve by factorizing x2+11x+24=0
(x+3)(x+8)=0
x=−3, −8
Which factoring pattern is shown? x2−36
Answer: What is a difference of squares?
Factored Form: (x+6)(x−6)