### Plot quadratic graphs, roots and turning points » More

#### Year 10/11 Solving quadratic equations maths revision

###### Finding roots and turning points - graphically

A turning point is where the gradient is zero.

To find the ROOTS of an equation you need to solve the equation to find the values of x.
If you have a graph, you can do this by finding where the graph cuts the x-axis.

If you have to deduce the roots of a quadratic equation algebraically, use methods like factorising or completing the square to solve the quadratic equation.

Q1: Write down the co-ordinates of the turning point and the two roots for this quadratic graph.

ANS

Quadratic equations are written as: y = x2 + 4x + 4

Sometimes we also write it like f(x) = x2 + 4x + 4

This is called function notation.

Plot the quadratic graph f(x) = x2 – 4x + 3

Q1: Use your graph to estimate the roots of the equation f(x) = x2 – 4x + 3 = 0

Q2: Write down the coordinates of the turning point of f(x)

Q3: Use your graph to estimate the values of x when f(x) = 2

ANS

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