Graphing Parabolas (3.15.4)

Question 1

• Standard form of a quadratic function: f (x) = ax^2+ bx + c.

• Vertex of a parabola: (h, k).
• h = –b/2a.
• k = f (h).

• Vertex form of a quadratic function: f (x) = a(x – h)^2 + k.

Answer 1

• Standard form of a quadratic function: f (x) = ax^2+ bx + c.

• Vertex of a parabola: (h, k).
• h = –b/2a.
• k = f (h).

• Vertex form of a quadratic function: f (x) = a(x – h)^2 + k.

Question 2

• To write a quadratic equation in standard form in vertex form:
• Find the value of h.
• Find the value of k.
• Substitute the values of a, h, and k into vertex form.

Answer 2

• To write a quadratic equation in standard form in vertex form:
• Find the value of h.
• Find the value of k.
• Substitute the values of a, h, and k into vertex form.

Question 3

This example is for a negative parabola – because a
coefficient is negative.
The vertex is shown in the expression: (–3, 2).
Remember: the x-value changes sign.
To find the x-intercepts, set everything equal to 0 and solve
for x.
These are the points where the curve crosses the x-axis.
Graph everything and you are done.

Answer 3

This example is for a negative parabola – because a
coefficient is negative.
The vertex is shown in the expression: (–3, 2).
Remember: the x-value changes sign.
To find the x-intercepts, set everything equal to 0 and solve
for x.
These are the points where the curve crosses the x-axis.
Graph everything and you are done.

Question 4

Since this equation is in standard form, find the vertex using
the formulas for h and k:
 h = –b/2a = –(–2)/2(1) = 1
 k = f (h) = f (1) = 1
2
–2(1) = 3 = 2
So the vertex is at (1, 2).
The parabola opens up since a is positive.

Answer 4

Since this equation is in standard form, find the vertex using
the formulas for h and k:
 h = –b/2a = –(–2)/2(1) = 1
 k = f (h) = f (1) = 1
2
–2(1) = 3 = 2
So the vertex is at (1, 2).
The parabola opens up since a is positive.

Question 5

With the vertex above the x-axis and the curve opening

upward, you know the curve will never cross the x-axis.

Answer 5

With the vertex above the x-axis and the curve opening

upward, you know the curve will never cross the x-axis.

Question 6

So look for the y-intercept. Solve f (x) for x = 0. This
y-value is where the curve will cross the y-axis. In this case,
that is the point (0, 3). The y-intercept is always at c

Answer 6

So look for the y-intercept. Solve f (x) for x = 0. This
y-value is where the curve will cross the y-axis. In this case,
that is the point (0, 3). The y-intercept is always at c

Question 7

Now, use the fact that a parabola has symmetry to help locate
a second point.
In this example, the y-intercept is to the left 1 unit and up 1
unit from the vertex. So, to graph your matching point, locate
the point that is to the right 1 unit and up 1 unit from the
vertex.

Answer 7

Now, use the fact that a parabola has symmetry to help locate
a second point.
In this example, the y-intercept is to the left 1 unit and up 1
unit from the vertex. So, to graph your matching point, locate
the point that is to the right 1 unit and up 1 unit from the
vertex.

Question 8

Now your curve is noted and you can draw it.

Answer 8

Now your curve is noted and you can draw it.