Question

foa/algebra 1
unit 3a: factoring & solving quadratic equations
notes
practice: identify the zeros of the functions:
a. ( y=(x + 4)(x + 3) )
b. ( f(x)=(x - 7)(x + 5) )
c. ( y=x(x - 9) )
d. ( f(x)=5(x - 4)(x + 8) )
practice: create an equation to represent the following graphs:
zeros: ( x=)__ & __
( y=)____
zeros: ( x=)__ & __
( y=)____
solving a quadratic equation really means:
the place(s) where the graph crosses the ( x -)axis has several names. they can be referred as:
__ __

Explanation:

Step1: Find zeros from graph

For the first graph, the parabola crosses the x - axis at \(x = 1\) and \(x = 3\).
For the second graph, the parabola crosses the x - axis at \(x = 2\) and \(x = 5\).

Step2: Form quadratic equation

The general form of a quadratic equation with zeros \(x=a\) and \(x = b\) is \(y=k(x - a)(x - b)\).
For the first graph, assume \(k = 1\), then \(y=(x - 1)(x - 3)=x^{2}-4x + 3\).
For the second graph, assume \(k=-1\) (because the parabola opens downwards), then \(y=-(x - 2)(x - 5)=-x^{2}+7x - 10\).

Answer:

For the first graph:
Zeros: \(x = 1\) & \(x = 3\)
\(y=(x - 1)(x - 3)\)
For the second graph:
Zeros: \(x = 2\) & \(x = 5\)
\(y=-(x - 2)(x - 5)\)
Solving a quadratic equation really means finding the x - values where \(y = 0\) (the points where the graph of the quadratic function crosses the x - axis).
The place(s) where the graph crosses the x - axis can be referred as: roots, solutions, x - intercepts, zeros.