1. Graphs of Quadratic Functions

2. We’ll use this graph of a quadratic function to walk through the different characteristics

3. Let’s start with the shape of quadratics…
Parabola
But this one isn’t
a function

4. a = narrows/widens the graph’s shape, further
𝒚=𝒂 𝒙 𝟐 +𝒃𝒙+𝒄
Where a, b, & c are real numbers
a ≠ 0
a = narrows/widens the graph’s shape, further
away from zero  the more narrow
opens it up (+a) or down (-a)
b = moves it horizontally; left (+b) or right (-b)
c = moves it vertically along the y-axis
up (+c) or down (-c)

5. X = -1.5 Line of symmetry x = # Fold that divides the
Parabola into matching
halves
Goes through the vertex
𝒙= −𝒃 𝟐𝒂
X = -1.5
Remember, an equation with no “y” and
Only an “x” represents a VERTICAL line.
HOY VUX

6. Where the parabola crosses the y-axis
“c”  y – intercept
(0, y) or (0, c)
𝒚=𝒂 (𝟎) 𝟐 +𝒃(𝟎)+𝒄
𝒚=𝟎+𝟎+𝒄
𝒚=𝒄

7. parabola crosses the x-axis
2 roots
1 root
The point(s) where
parabola crosses the x-axis
Also called the solutions,
Roots, or zeros
Usually has 2 x-intercepts, but
could also have 1 or
no real roots
NO real roots

8. “+a”  minimum because parabola opens up
The highest (maximum) OR
the lowest (minimum) point on the
parabola
“+a”  minimum because parabola
opens up
“-a”  maximum because parabola
opens down