# A18c – Solving quadratic equations using the quadratic formula

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# The quadratic formula

$${\color{Black}{\large \text{If }ax^{2} + bx +c = 0}}$$

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$${\color{Black}{\large \text{then }x = \dfrac{-b \pm \sqrt{b^{2}-4ac}}{2a}}}$$

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$${\large \color{#e0e0e0}{\text{then x }}\color{Black}{= \dfrac{-b}{2a} \pm \dfrac{\sqrt{b^{2}-4ac}}{2a}}}$$

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$${\color{Black}{\large \text{The line }x = -\dfrac{b}{2a}\text{ is the line }}}$$$${\color{Black}{\large \text{of symmetry for the curve }}}$$ $${\color{Black}{\large y=ax^{2} + bx +c}}$$

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$${\color{Black}{\large \text{Also, }\dfrac{\sqrt{b^{2}-4ac}}{a} \text{ is the }}}$$ $${\color{Black}{\large \text{distance between the }}}$$ $${\color{Black}{\large \text{solutions of }ax^{2} + bx +c = 0 }}$$. $${\color{Black}{\large \text{Can you see why?}}}$$

# Solving quadratic equations using the quadratic formula

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