اختبار اختيار من متعدد تفاعلي: Quadratic Formula & The Discriminant Worksheet - Reveal
This worksheet focuses on the quadratic formula and the discriminant. It includes questions on identifying the discriminant formula, determining the number and type of roots based on the discriminant value, and solving various quadratic equations. Students will practice working with real and imaginary roots, as well as understanding the graphical significance of setting quadratic equations to zero to find x-intercepts.
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اختبار شهادة تدريبي مؤقت للصف والمادة والفصل نفسه.
اختر إجابة واحدة لكل سؤال. عند الاختيار ستظهر النتيجة فورًا: الأخضر صحيح، والأحمر خطأ، وسيظهر تفسير الإجابة مباشرة إن كان متوفرًا. وبعد آخر سؤال ستظهر الدرجة النهائية تلقائيًا.
The discriminant of a quadratic equation in the form ax2 + bx + c = 0 is defined as b2 - 4ac.
Question 2
Points: 1
Determine the value of the discriminant and describe the number and type roots for the following: x2 + 7x + 13
Explanation
For the equation x2 + 7x + 13, a=1, b=7, c=13. The discriminant is b2 - 4ac = 72 - 4(1)(13) = 49 - 52 = -3. Since the discriminant is negative, there are two imaginary roots.
Question 3
Points: 1
Use the quadratic formula to solve 2x2 + 2x - 12.
Explanation
Simplifying 2x2 + 2x - 12 = 0 by dividing by 2 gives x2 + x - 6 = 0. Factoring gives (x+3)(x-2) = 0, so x = 2 and x = -3.
Question 4
Points: 1
If the discriminant is negative, then the quadratic has:
Explanation
A negative discriminant means the term under the square root in the quadratic formula is negative, resulting in two complex (imaginary) solutions.
Question 5
Points: 1
The quadratic equation can be used to solve quadratic equations that can or cannot be factored.
Explanation
The quadratic formula is a universal method that can solve any quadratic equation, whether it is factorable or not.
Question 6
Points: 1
Solve the equation 2p2 - 3p - 3 = 0 using the Quadratic Formula.
Explanation
Using the formula \(\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\) with a=2, b=-3, c=-3: \(\frac{3 \pm \sqrt{(-3)^2 - 4(2)(-3)}}{2(2)} = \frac{3 \pm \sqrt{9 + 24}}{4} = \frac{3 \pm \sqrt{33}}{4}\).
Question 7
Points: 1
Solve using the quadratic formula: f(x) = 2x2 - 4x + 7
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