- Write the equation in standard form and identify a, b, and c.
- Determine whether the parabola opens up or down.
- Find the vertex and determine whether it is the maximum or minimum point.
- Make a rough sketch of the parabola.
- Example 1
- Example 2
This equation is already in standard form.
y = 2x2 – 4x – 5
a = 2, b = –4, c = –5
Since a is positive, this parabola opens up.
x = 
= 
= 
= 1
To find the y-coordinate, substitute the x value of 1 into the quadratic equation and solve
for y.
y = 2x2 – 4x – 5
y = 2(1)2 – 4(1) – 5
y = 2 – 4 – 5
y = –7
The vertex is (1, –7).
Because this parabola opens up, the vertex is the minimum point.
y + 1 = –x2 + 4x
–1 –1
y = –x2 + 4x – 1 This is the standard form.
Now for the values of a, b, and c.
y = –1x2 + 4x – 1
a = –1, b = 4, c = –1
Since a is negative, this parabola opens down.
x = 
= 
= 
= 2
To find the y-coordinate, substitute the x value of 2 into the quadratic equation, and
solve for y.
y = –x2 + 4x – 1
y = –1(2)2 + 4(2) – 1
y = –1(4) + 8 – 1
y = –4 + 8 – 1
y = 3
The vertex is (2, 3).
Because this parabola opens down, the vertex is the maximum point.
