Question

When the quadratic function y = 2x^2 - 5x - 3 is written in Factored Form it takes the form of y = (mx + n)(x + p). Where the values of m, n and p are as follows.

Answer 1

To write the quadratic function in factored form, we need to find the roots of the quadratic equation.

The equation y = 2x^2 - 5x - 3 can be factored as:

y = (2x + 1)(x - 3)

So, m = 2, n = 1, and p = -3.

Answer 2

Write a function in Standard Form for the parabola that has an axis of symmetry at x = 5, an x-intercept at 4 and passes through the point (5.5, 1.5).

Answer 3

To find a quadratic function in standard form for a parabola with these characteristics, we can start by identifying the vertex of the parabola, which lies on the axis of symmetry at x = 5.

Since the x-intercept is given as 4, that means the parabola intersects the x-axis at (4, 0).

Now, let's use the vertex form of a quadratic function to find the equation:

y = a(x - h)^2 + k

where (h, k) is the vertex of the parabola.

Since the axis of symmetry is x = 5, the value of h is 5.

Therefore, we have:

y = a(x - 5)^2 + k

To find the value of a and k, we can substitute the coordinates of the given point (5.5, 1.5) into the equation:

1.5 = a(5.5 - 5)^2 + k

Simplifying, we get:

1.5 = a(0.5)^2 + k
1.5 = 0.25a + k

or

k = 1.5 - 0.25a

Now, we substitute the coordinates of the x-intercept (4, 0) into the equation:

0 = a(4 - 5)^2 + k

Simplifying, we get:

0 = a(1)^2 + k
0 = a + k

or

k = -a

Now we put the values we obtained for k in terms of a together:

- a = 1.5 - 0.25a

Add 0.25a to each side:

- a + 0.25a = 1.5 - 0.25a + 0.25a

- 0.75a = 1.5

Divide each side by -0.75:

a = -2

Substituting the value of a = -2 into the equation k = -a:

k = -(-2) = 2

Therefore, the equation of the parabola in standard form is:

y = -2(x - 5)^2 + 2

Answer 4

What is the vertex of the function y = 11(x-13)^2 + 16?

Answer 5

The vertex of a quadratic function in the form y = a(x - h)^2 + k is given by the coordinates (h, k). For the function y = 11(x - 13)^2 + 16, the vertex is located at the point (13, 16).

Answer 6

The axis of symmetry for the parabola that corresponds to
y = - 1/2(x - 2)^2 + 16 is x=2?

Answer 7

No, the axis of symmetry for the parabola that corresponds to the equation y = -1/2(x - 2)^2 + 16 is x = 2. The x-coordinate of the vertex represents the axis of symmetry. In this case, the vertex has coordinates (2, 16), so the axis of symmetry is x = 2.

Answer 8

Consider the quadratic function y = 7(x - 5.5)^2 - 9.

The parabola that represents this function has a ___ value that is equal to ___.

The range of this parabola can be described as ___ ___.

Answer 9

The parabola that represents the quadratic function y = 7(x - 5.5)^2 - 9 has a coefficient of the squared term (7) that is positive.

The value of the coefficient affects the shape of the parabola. Since it is positive, the parabola opens upwards.

The value of the constant term (-9) represents the y-intercept, which is the point where the parabola intersects the y-axis. In this case, the y-intercept is at (0, -9).

The range of this parabola can be described as "all real numbers greater than or equal to -9." This is because the parabola opens upwards, and the vertex is the lowest point on the graph, which occurs at (-9).

Answer 10

The vertex of a parabola is located at (3, -7). The parabola also travels through the point (-1, 5). What is the value of the parameter a in Vertex Form?

Answer 11

In vertex form, the equation of a parabola is given by: y = a(x - h)^2 + k, where (h, k) represents the vertex.

Given that the vertex is located at (3, -7), we have: y = a(x - 3)^2 - 7.

The parabola also passes through the point (-1, 5), which means that when x = -1, y = 5:

5 = a(-1 - 3)^2 - 7
5 = a(-4)^2 - 7
5 = 16a - 7
16a = 12
a = 12/16
a = 3/4

Therefore, the value of the parameter "a" in vertex form is 3/4.

Answer 12

Write the function equation that represents the parabola with a vertex at (10, 32) and passes through the point (-2, -4) in Standard Form.
[HINT: Your first step is to find a]