U4HW4: Standard Form of Quadratic Functions
Quadratic Functions Day 4 Homework
1. Use diamonds to factor the following quadratic functions given in standard form.
a. 𝑥 ! + 3𝑥 − 28
b. 𝑥 ! + 13𝑥 + 42
c. 𝑥 ! + 3𝑥 + 2 d. 𝑥 ! − 4𝑥 + 12
2. Graphing a quadratic function without the aid of a calculator
a) Find the x-intercepts of 𝑦 = 𝑥 ! − 2𝑥 − 8 by factoring (use a diamond if you need to help).
b) What is the x-coordinate of the vertex of 𝑦 = 𝑥 ! − 2𝑥 − 8? What is the equation of the axis of
symmetry? Use the intercepts that you found and symmetry of the parabola to find these.
c) Now find the y-coordinate by utilizing the fact that you know the input value for any point on the yaxis.
d) Graph the function on a grid, include at least five points on your graphs.
e) Repeat this process (steps a-d) for the quadratic function: 𝑦 = 𝑥 ! + 2𝑥 − 15.
3. Using Vertex Form (f(x) = a(x - h)2 + k). Use your understanding of transformations to write the
equation for the function whose graph is shown. The graph of y = x2 has been provided on the same
axes. Only use your calculator as a check once you’ve figured out the equation by hand.
a.
b.
3
y
3
2
2
1
1
y
x
−3
−2
−1
1
2
x
3
−3
−2
−1
−1
−1
−2
−2
−3
−3
c.
1
2
3
1
2
3
d.
y
3
y
4
3
2
2
1
1
x
−4
−3
−2
−1
1
2
3
4
x
5
−3
−2
−1
−1
−1
−2
−3
−2
−4
−3
U4HW4: Standard Form of Quadratic Functions
4. Write equations for the graphs below using factored/standard form, or vertex form. (don’t forget about the “a”
value!!!)
a.
b.
c.
d.