From left to right, the line slants upwards like in this image:
Plot the x-intercept(s), y-intercept, vertex, and axis of symmetry for the function below.
2 answers:
<span>Given a quadratic equations:
g(x) = x</span>²<span> + 4x + 3
The equation cannot be factored as it's not a complete square.
therefore using the vertex form of a quadratic equation we will convert the equation into its vertex form and hence it's easy to graph a quadratic equation in vertex form.
The vertex for is :
g(x) = a(x - h)</span>² + k
where,
'h' is the axis of symmetry and (h,k) is the vertex.
So from the given equation we will rewrite the equation as:
x² + 4x + 3 = 0
x² + 4x = -3
x² + 4x + (2)² = -3 + (2)²
(x + 2)² = -3 + 4
(x + 2)² = 1
(x + 2)² - 1 = 0
Hence,
h = -2
and
k = -1
Thus our line of symmetry is x = -2 and vertex is (h,k) = (-2,-1)
Now,
we will find the x intercepts,
using the equation,
(x + 2)² = 1
square root on both sides,
√(x + 2)² = √1
x + 2 = <span>± 1
x = 1 - 2
x = -1
or
x = -1 - 2
x = -3
For y-intercept put x = 0 into the real equation:
</span>g(x) = 0² + 4(0) + 3
y = 3
g(x) = x</span>²<span> + 4x + 3
The equation cannot be factored as it's not a complete square.
therefore using the vertex form of a quadratic equation we will convert the equation into its vertex form and hence it's easy to graph a quadratic equation in vertex form.
The vertex for is :
g(x) = a(x - h)</span>² + k
where,
'h' is the axis of symmetry and (h,k) is the vertex.
So from the given equation we will rewrite the equation as:
x² + 4x + 3 = 0
x² + 4x = -3
x² + 4x + (2)² = -3 + (2)²
(x + 2)² = -3 + 4
(x + 2)² = 1
(x + 2)² - 1 = 0
Hence,
h = -2
and
k = -1
Thus our line of symmetry is x = -2 and vertex is (h,k) = (-2,-1)
Now,
we will find the x intercepts,
using the equation,
(x + 2)² = 1
square root on both sides,
√(x + 2)² = √1
x + 2 = <span>± 1
x = 1 - 2
x = -1
or
x = -1 - 2
x = -3
For y-intercept put x = 0 into the real equation:
</span>g(x) = 0² + 4(0) + 3
y = 3
You might be interested in
Answer:
67.5feet
Step-by-step explanation:
Given parameters:
Model distance between building and gymnasium = 22.5 inches
Scale of model : 1 inch = 3 feet
Unknown:
Actual ground distance = ?
To solve this problem, we first must understand the concept of scale. A scale is a relationship that represents a dimension on a map/model compared to the true ground expression. In order to visualize or represent some real life objects on paper or in a computer, we use models. These models are an abstraction of the real world based on scales. There are different ways of representing a scale.
In this problem;
the scale is given as;
1 inch on model represents 3 feet on ground
Now, to find 22.5 inches, simply cross multiply and solve;
If 1 inch on model represents 3 feet on ground
22.5 inches on a model will be =
= 67.5feet
Therefore, the actual distance is 67.5feet