Find vertex of a quadratic equation

kittyslut SG

How to find the vertex of y = 2x^2 - 7? Pls teach me. thanks

eagle SG

do u mean the turning point?

You can either differentitate and set it to zero to find x
sub x back to the original equation to find y

complete the square

kittyslut SG

can i use x = -b/2a to find the vertex?

eagle SG

sounds good, can also

Lee012lee SG

can i use x = -b/2a to find the vertex?

Quadratic Function

y = ax^2 + bx + c

Differentiate it

dy/dx = 2ax + b

For stationary point , 2ax + b = 0

x = - b / (2a)

If a > 0, substitute x = - b / (2a) into y to find the min y value

If a < 0, substitute x = - b / (2a) into y to find the max y value

This method of finding max y or min y value is not taught in "O" level maths textbooks.

But this is a very useful method that should be taught to "O" level maths students especially "O" level E.Maths students who do not learn differentiation ie to teach them that

For the quadratic function, y = ax^2 + bx + c

If a > 0, substitute x = - b / (2a) into y to find the min y value

If a < 0, substitute x = - b / (2a) into y to find the max y value

PS : This method is frequently used by China students.

eagle SG

one can easily derive the x value from the middle of the x values of the 2 roots as well :)

Lee012lee SG

one can easily derive the x value from the middle of the x values of the 2 roots as well :)

Indeed, for drawing the turning point in a curve (especially in drawing a smooth curve question), many E.Maths teachers simply tell their students to find the middle value x of the 2 x-intercepts and then substitute this middle x value into the y to find the min y or max y.