17.4 What is ‘c’ in a Quadratic Equation?

17.4 What is $c$ in a Quadratic Equation?

In the quadratic equation$$y=ax^2+bx+c$$

the c is the constant term.

It is the number that does not have $x$ beside it.

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🟦 What does $c$ tell us?

The value of $c$ gives the y-intercept of the quadratic graph.

The y-intercept is the point where the parabola crosses the y-axis.

On the y-axis:$$x=0$$

So if:$$y=ax^2+bx+c$$

substitute $x=0$:$$y=a(0)^2+b(0)+c$$$$y=c$$

Therefore, the y-intercept is:$$(0,c)$$

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🟩 Example

Consider:$$y=x^2-4x+3$$

Compare it with:$$y=ax^2+bx+c$$

So:$$a=1,\qquad b=-4,\qquad c=3$$

Therefore:$$c=3$$

and the y-intercept is:$$(0,3)$$

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🟪 Another Example

Consider:$$y=2x^2+5x-7$$

Here:$$c=-7$$

So the graph crosses the y-axis at:$$(0,-7)$$

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💡 Easy Way to Remember

For:$$y=ax^2+bx+c$$

• $a$ controls the direction and width of the parabola.
• $b$ helps locate the turning point and line of symmetry.
• $c$ gives the y-intercept.