Mathematics, 06.05.2021 14:00 cookies1164
Quadratic function, or the vertex form of a quadratic function.
The standard form of a quadratic function (a parabola) is:
y = ax² + bx + c
The vertex form of a quadratic function (a parabola) is:
y = a(x – h)² + k
The quadratic function for a parabola in standard form can be converted to vertex form by completing the square.
I am going to use the standard form of a quadratic function:
y = ax² + bx + c
The standard form of quadratic equation would be:
ax² + bx + c = 0
Solve for x using the quadratic formula:
x = (-b/2a) ± [√(b² - 4ac)/2a]
the axis of symmetry (the x coordinate of the vertex) of the parabola is:
x_axis_of_symmetry = (-b/2a)
Since the axis of symmetry must be x = 1:
(-b/2a) = x_axis_of_symmetry
(-b/2a) = 1
Choose any value for a, and then solve for b
Or
Choose any value for b, and then solve for a
As an example, since the parabola must open downward, a must be negative.
let a = -1
(a = -1 is an arbitrary choice. You can choose any value for “a”, as long as it is a negative value.)
(-b/2a) = 1
-b/[2*(-1)] = 1
-b/(-2) = 1
b/(2) = 1
[b/(2)]*(2) = 1*(2)
b*(2/2) = 1*2
b*(1) = 1*2
b = 2
y = ax² + bx + c
substituting the values a = -1 and b = 2
y = -1*x² + 2*x + c
y = -x² + 2x + c
you can now choose a value for c
Strictly speaking, you can choose any value for “c”. However, your problem statement asks that you compute the x-intercepts. “c” must be a positive value for the quadratic function to cross the x-axis. So I recommend you choose a positive value for “c”.
for example, let c = 5
using the values a = -1, b = 2, and c = 5
>>> The standard form of the final quadratic function is:
y = -x² + 2x + 5
>>> The standard form of the final quadratic equation is:
0 = -x² + 2x + 5
>>> The vertex form of the final quadratic function is:
y = -(x – 1)² + 6
>>> The vertex form of the final quadratic equation is:
0 = -(x – 1)² + 6
kelsey your question
Answers: 2
Mathematics, 21.06.2019 21:30, karmaxnagisa20
Three friends went on a road trip from phoenix, az, to san diego, ca. mark drove 50 percent of the distance. jason drove 1/8 of the distance. andy drove the remainder of the distance. 1. andy thinks he drove 1/4 of the distance from phoenix, az, to san diego, ca. is andy correct? 2. the distance from phoenix, az, to san diego, ca, is 360 miles. how many miles did each person drive? 3. solve the problem. what is the answer in total?
Answers: 3
Mathematics, 21.06.2019 22:10, ansonferns983
Given: ae ≅ ce ; de ≅ be prove: abcd is a parallelogram. we have that ab || dc. by a similar argument used to prove that △aeb ≅ △ced, we can show that △ ≅ △ceb by. so, ∠cad ≅ ∠ by cpctc. therefore, ad || bc by the converse of the theorem. since both pair of opposite sides are parallel, quadrilateral abcd is a parallelogram.
Answers: 1
Mathematics, 22.06.2019 03:50, morkitus13
The image of abc is a'b'c. what transformations would result in this image? abc is reflected over the line x = 1, then is rotated -90° around the origin. abc is reflected over the line y = x - 1, then t: (x, y) → (x - 1, y - 1). abc is rotated 90° around the origin, then is reflected over the y-axis. abc is rotated -90° around the origin, then is reflected over the line y = -1.
Answers: 2
Quadratic function, or the vertex form of a quadratic function.
The standard form of a quadratic f...
Mathematics, 02.02.2021 22:40
Chemistry, 02.02.2021 22:40
Chemistry, 02.02.2021 22:40
Social Studies, 02.02.2021 22:40
Mathematics, 02.02.2021 22:40