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Please find the equation of the quadratic

Please Find The Equation Of The Quadratic class=

Sagot :

Answer:

y = 4(x - 3)² - 5

Step-by-step explanation:

Given the vertex, (3, -5), and the other point, (4, -1):

Substitute these values into the vertex form of the quadratic equation:

y = a(x - h)² + k

where:

(h, k) = vertex

a = determines the direction of which the graph opens (if a > 1, the graph opens up; a < 1, the graph opens down). The value of a also determines the width of the parabola.  If 0 < a < 1, the graph will be wide; if a > 1, the graph will be narrow.

h = indicates a horizontal translation.

k = indicates a vertical translation.

Next, substitute the values of the vertex, (3, -5), and the other given point, (4, -1) into the vertex form and solve for the value of a:

y = a(x - h)² + k

-1 = a(4 - 3)² - 5

-1 = a( 1 )² - 5

-1 + 5 = a1 - 5 + 5

4 = a

Therefore, the equation of the given graph is: y = 4(x - 3)² - 5.  

Note:

If the  equation needs to be in standard form, ax² + bx + c, simply expand the binomial factors in the vertex form, and combine like terms.  Doing so will result in the following standard form: y = 4x² - 24x + 31.