Respuesta :
Answer:
y = [tex]\frac{1}{2}[/tex](x - 5)² - 2
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (5, - 2), thus
y = a(x - 5)² - 2
To find a substitute (7, 0) into the equation
0 = a(7 - 5)² - 2
0 = 4a - 2 ( add 2 to both sides )
2 = 4a ( divide both sides by 4 )
a = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]
y = [tex]\frac{1}{2}[/tex] (x - 5)² - 2 ← in vertex form
Quadratic function with vertex (5, -2) and passing through (7, 0) will be [tex]f(x)=\frac{1}{2}(x-5)^2-2[/tex].
Quadratic function:
- Equation of a quadratic function in the vertex form is given by,
f(x) = a(x - h)² + k
Here, (h, k) is the vertex of the parabola representing the quadratic
function.
Given in the question,
- Vertex of the quadratic function → (5, -2)
- Parabola passes through a point (7, 0).
Substitute the vertex in the quadratic function,
f(x) = a(x - 5)² - 2
Since, this parabola passes through a point (7, 0),
0 = a(7- 5)² - 2
0 = 4a - 2
a = [tex]\frac{1}{2}[/tex]
Equation of the quadratic function will be,
f(x) = [tex]\frac{1}{2}(x-5)^2-2[/tex]
Hence, equation of the quadratic function will be → [tex]f(x)=\frac{1}{2}(x-5)^2-2[/tex]
Learn more about the quadratic function here,
https://brainly.com/question/13148055?referrer=searchResults
